Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 5

Rational Number Arithmetic

Lesson 7: Adding and Subtracting to Solve Problems

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topics
Video Definition 30--Rationals and Radicals--Radical Simplification (Spanish Audio) Video Definition 30--Rationals and Radicals--Radical Simplification (Spanish Audio) Video Definition 30--Rationals and Radicals--Radical Simplification (Spanish Audio)

Topic

Rationals and Radicals

Description

Simplifying a radical expression involves factoring out terms to find whole number factors. Examples simplify √360 into 6 * √10 and √288 into 12 * √2. Provides techniques for simplifying radicals, a key skill in manipulating and solving radical expressions.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 31--Rationals and Radicals--Radical Symbol Video Definition 31--Rationals and Radicals--Radical Symbol Video Definition 31--Rationals and Radicals--Radical Symbol

Topic

Rationals and Radicals

Description

The Radical Symbol is used to find a specified root of a number or expression. Examples include square roots (√2) and cube roots (³√5). It connects to fractions by identifying roots in rational forms. Introduces the concept of radicals and their importance in mathematical expressions.

Radical Expressions
Video Definition 31--Rationals and Radicals--Radical Symbol (Spanish Audio) Video Definition 31--Rationals and Radicals--Radical Symbol (Spanish Audio) Video Definition 31--Rationals and Radicals--Radical Symbol (Spanish Audio)

Topic

Rationals and Radicals

Description

The Radical Symbol is used to find a specified root of a number or expression. Examples include square roots (√2) and cube roots (³√5). It connects to fractions by identifying roots in rational forms. Introduces the concept of radicals and their importance in mathematical expressions.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 32--Rationals and Radicals--Radicand Video Definition 32--Rationals and Radicals--Radicand Video Definition 32--Rationals and Radicals--Radicand

Topic

Rationals and Radicals

Description

Radicand refers to the number or expression under the radical symbol, such as 5 in √5. This is fundamental for identifying what part of a fraction or term is being rooted. Builds on the radical concept by focusing on the specific part of the radical expression being evaluated.

Radical Expressions
Video Definition 32--Rationals and Radicals--Radicand (Spanish Audio) Video Definition 32--Rationals and Radicals--Radicand (Spanish Audio) Video Definition 32--Rationals and Radicals--Radicand (Spanish Audio)

Topic

Rationals and Radicals

Description

Radicand refers to the number or expression under the radical symbol, such as 5 in √5. This is fundamental for identifying what part of a fraction or term is being rooted. Builds on the radical concept by focusing on the specific part of the radical expression being evaluated.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 33--Rationals and Radicals--Rational Equations Video Definition 33--Rationals and Radicals--Rational Equations Video Definition 33--Rationals and Radicals--Rational Equations

Topic

Rationals and Radicals

Description

Rational Equations are equations involving fractions where both sides include variables. These often involve steps to solve for variables, like x in (2x + 6) / (x - 3) = 5. Extends the use of fractions by incorporating variables, creating a bridge between fractions and algebra.

Rational Functions and Equations
Video Definition 33--Rationals and Radicals--Rational Equations (Spanish Audio) Video Definition 33--Rationals and Radicals--Rational Equations (Spanish Audio) Video Definition 33--Rationals and Radicals--Rational Equations (Spanish Audio)

Topic

Rationals and Radicals

Description

Rational Equations are equations involving fractions where both sides include variables. These often involve steps to solve for variables, like x in (2x + 6) / (x - 3) = 5. Extends the use of fractions by incorporating variables, creating a bridge between fractions and algebra.

This video includes Spanish audio and can be used with multilingual learners.

Rational Functions and Equations
Video Definition 34--Rationals and Radicals--Rational Exponent Video Definition 34--Rationals and Radicals--Rational Exponent Video Definition 34--Rationals and Radicals--Rational Exponent

Topic

Rationals and Radicals

Description

A Rational Exponent rewrites radicals without symbols, like √2 as 2(1/2). This demonstrates how radicals are expressed in exponent notation in equations. Connects radicals to exponent notation, providing a versatile way to express roots.

Rational Expressions
Video Definition 34--Rationals and Radicals--Rational Exponent (Spanish Audio) Video Definition 34--Rationals and Radicals--Rational Exponent (Spanish Audio) Video Definition 34--Rationals and Radicals--Rational Exponent (Spanish Audio)

Topic

Rationals and Radicals

Description

A Rational Exponent rewrites radicals without symbols, like √2 as 2(1/2). This demonstrates how radicals are expressed in exponent notation in equations. Connects radicals to exponent notation, providing a versatile way to express roots.

This video includes Spanish audio and can be used with multilingual learners.

Rational Expressions
Video Definition 35--Rationals and Radicals--Rational Expressions Video Definition 35--Rationals and Radicals--Rational Expressions Video Definition 35--Rationals and Radicals--Rational Expressions

Topic

Rationals and Radicals

Description

Rational Expressions are ratios of two polynomials, such as (x + 1) / (x - 1). They demonstrate how polynomials can form fractions with numerical denominators. Demonstrates how polynomials form the basis for more complex fractional expressions.

Rational Expressions
Video Definition 35--Rationals and Radicals--Rational Expressions (Spanish Audio) Video Definition 35--Rationals and Radicals--Rational Expressions (Spanish Audio) Video Definition 35--Rationals and Radicals--Rational Expressions (Spanish Audio)

Topic

Rationals and Radicals

Description

Rational Expressions are ratios of two polynomials, such as (x + 1) / (x - 1). They demonstrate how polynomials can form fractions with numerical denominators. Demonstrates how polynomials form the basis for more complex fractional expressions.

This video includes Spanish audio and can be used with multilingual learners.

Rational Expressions
Video Definition 36--Rationals and Radicals--Rational Functions Video Definition 36--Rationals and Radicals--Rational Functions Video Definition 36--Rationals and Radicals--Rational Functions

Topic

Rationals and Radicals

Description

Rational Functions are ratios between two polynomial functions, such as f(x) = x / (x + 1). They showcase how algebra creates equations that are fractions and functions. Highlights how functions can also be expressed as ratios, blending fractions and algebraic functions.

Rational Functions and Equations
Video Definition 36--Rationals and Radicals--Rational Functions (Spanish Audio) Video Definition 36--Rationals and Radicals--Rational Functions (Spanish Audio) Video Definition 36--Rationals and Radicals--Rational Functions (Spanish Audio)

Topic

Rationals and Radicals

Description

Rational Functions are ratios between two polynomial functions, such as f(x) = x / (x + 1). They showcase how algebra creates equations that are fractions and functions. Highlights how functions can also be expressed as ratios, blending fractions and algebraic functions.

This video includes Spanish audio and can be used with multilingual learners.

Rational Functions and Equations
Video Definition 37--Rationals and Radicals--Rational Numbers Video Definition 37--Rationals and Radicals--Rational Numbers Video Definition 37--Rationals and Radicals--Rational Numbers

Topic

Rationals and Radicals

Description

Rational Numbers are fractions expressed as a/b, such as 1 / 4 or 2 / 3. These are critical in understanding all fraction constructions. Provides a foundational understanding of fractions as ratios of integers, essential for all rational concepts.

Understanding this video is essential for grasping the fundamentals of Rationals and Radicals. The mathematical concepts explored here form the basis for further exploration and application in related fields.

Rational Functions and Equations
Video Definition 37--Rationals and Radicals--Rational Numbers (Spanish Audio) Video Definition 37--Rationals and Radicals--Rational Numbers (Spanish Audio) Video Definition 37--Rationals and Radicals--Rational Numbers (Spanish Audio)

Topic

Rationals and Radicals

Description

Rational Numbers are fractions expressed as a/b, such as 1 / 4 or 2 / 3. These are critical in understanding all fraction constructions. Provides a foundational understanding of fractions as ratios of integers, essential for all rational concepts.

This video includes Spanish audio and can be used with multilingual learners.

Rational Functions and Equations
Video Definition 38--Rationals and Radicals--Rationalizing a Radical Video Definition 38--Rationals and Radicals--Rationalizing a Radical Video Definition 38--Rationals and Radicals--Rationalizing a Radical

Topic

Rationals and Radicals

Description

Rationalizing a Radical removes roots by using conjugates such as (√3) * (√3). The process connects radicals to polynomials and simplifies rational expressions. Shows how to simplify radical expressions, making them more usable in equations and calculations.

Radical Expressions
Video Definition 38--Rationals and Radicals--Rationalizing a Radical (Spanish Audio) Video Definition 38--Rationals and Radicals--Rationalizing a Radical (Spanish Audio) Video Definition 38--Rationals and Radicals--Rationalizing a Radical (Spanish Audio)

Topic

Rationals and Radicals

Description

Rationalizing a Radical removes roots by using conjugates such as (√3) * (√3). The process connects radicals to polynomials and simplifies rational expressions. Shows how to simplify radical expressions, making them more usable in equations and calculations.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 39--Rationals and Radicals--Rationalizing an Expression Video Definition 39--Rationals and Radicals--Rationalizing an Expression Video Definition 39--Rationals and Radicals--Rationalizing an Expression

Topic

Rationals and Radicals

Description

Rationalizing an Expression involves removing radicals in the denominator by multiplying by a conjugate term. For example, 1 / (√2 + 1) is rationalized by multiplying by (√2 - 1). Focuses on simplifying expressions to remove radicals, aiding in creating standard forms for fractions.

Rational Functions and Equations
Video Definition 39--Rationals and Radicals--Rationalizing an Expression (Spanish Audio) Video Definition 39--Rationals and Radicals--Rationalizing an Expression (Spanish Audio) Video Definition 39--Rationals and Radicals--Rationalizing an Expression (Spanish Audio)

Topic

Rationals and Radicals

Description

Rationalizing an Expression involves removing radicals in the denominator by multiplying by a conjugate term. For example, 1 / (√2 + 1) is rationalized by multiplying by (√2 - 1). Focuses on simplifying expressions to remove radicals, aiding in creating standard forms for fractions.

This video includes Spanish audio and can be used with multilingual learners.

Rational Functions and Equations
Video Definition 4--Rationals and Radicals--Conjugate of a Radical Video Definition 4--Rationals and Radicals--Conjugate of a Radical Video Definition 4--Rationals and Radicals--Conjugate of a Radical

Topic

Rationals and Radicals

Description

The conjugate of a radical is a factor that eliminates radicals in an expression. For example, the conjugate of √2 is √2, and the conjugate of (1 + √2) is (1 - √2), leading to simplified results like 1 - 2 = -1. Conjugates are used to rationalize denominators and simplify expressions involving radicals.

Radical Expressions
Video Definition 4--Rationals and Radicals--Conjugate of a Radical (Spanish Audio) Video Definition 4--Rationals and Radicals--Conjugate of a Radical (Spanish Audio) Video Definition 4--Rationals and Radicals--Conjugate of a Radical (Spanish Audio)

Topic

Rationals and Radicals

Description

The conjugate of a radical is a factor that eliminates radicals in an expression. For example, the conjugate of √2 is √2, and the conjugate of (1 + √2) is (1 - √2), leading to simplified results like 1 - 2 = -1. Conjugates are used to rationalize denominators and simplify expressions involving radicals.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 40--Rationals and Radicals--Rationalizing the Denominator Video Definition 40--Rationals and Radicals--Rationalizing the Denominator Video Definition 40--Rationals and Radicals--Rationalizing the Denominator

Topic

Rationals and Radicals

Description

Rationalizing the Denominator removes radicals from the denominator by multiplying by its conjugate. For example, 1 / √2 becomes √2 / 2 after rationalization. Illustrates how rationalization is used to make fractions easier to interpret and solve.

Radical Expressions
Video Definition 40--Rationals and Radicals--Rationalizing the Denominator (Spanish Audio) Video Definition 40--Rationals and Radicals--Rationalizing the Denominator (Spanish Audio) Video Definition 40--Rationals and Radicals--Rationalizing the Denominator (Spanish Audio)

Topic

Rationals and Radicals

Description

Rationalizing the Denominator removes radicals from the denominator by multiplying by its conjugate. For example, 1 / √2 becomes √2 / 2 after rationalization. Illustrates how rationalization is used to make fractions easier to interpret and solve.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression

Topic

Rationals and Radicals

Radical Expressions
Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression (Spanish Audio) Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression (Spanish Audio) Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression (Spanish Audio)

Topic

Rationals and Radicals

Radical Expressions
Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression

Topic

Rationals and Radicals

Rational Expressions
Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression (Spanish Audio) Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression (Spanish Audio) Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression (Spanish Audio)

Topic

Rationals and Radicals

Rational Expressions
Video Definition 43--Rationals and Radicals--Square Root Video Definition 43--Rationals and Radicals--Square Root Video Definition 43--Rationals and Radicals--Square Root

Topic

Rationals and Radicals

Description

A Square Root is a number that, when multiplied by itself, equals a given number. Square roots can be written using the radical symbol or as a rational exponent. For example, √25 = 5 and 36(1/2) = 6. This definition includes properties such as √a * √a = a. This term connects to the topic by introducing square roots, which are frequently encountered in operations involving radicals and rational expressions.

Radical Expressions
Video Definition 43--Rationals and Radicals--Square Root (Spanish Audio) Video Definition 43--Rationals and Radicals--Square Root (Spanish Audio) Video Definition 43--Rationals and Radicals--Square Root (Spanish Audio)

Topic

Rationals and Radicals

Description

A Square Root is a number that, when multiplied by itself, equals a given number. Square roots can be written using the radical symbol or as a rational exponent. For example, √25 = 5 and 36^(1/2) = 6. This definition includes properties such as √a * √a = a. This term connects to the topic by introducing square roots, which are frequently encountered in operations involving radicals and rational expressions.

Radical Expressions
Video Definition 44--Rationals and Radicals--Square Root Property Video Definition 44--Rationals and Radicals--Square Root Property Video Definition 44--Rationals and Radicals--Square Root Property

Topic

Rationals and Radicals

Description

The Square Root Property states that if a2 = b, then a = ±√b. Examples include 52 = 25, so √25 = ±5, and 62 = 36, so √36 = ±6. This property provides the basis for solving quadratic equations and simplifying radical expressions, tying back to the earlier concepts of radicals.

Radical Expressions
Video Definition 44--Rationals and Radicals--Square Root Property (Spanish Audio) Video Definition 44--Rationals and Radicals--Square Root Property (Spanish Audio) Video Definition 44--Rationals and Radicals--Square Root Property (Spanish Audio)

Topic

Rationals and Radicals

Description

The Square Root Property states that if a2 = b, then a = ±√b. Examples include 52 = 25, so √25 = ±5, and 62 = 36, so √36 = ±6. This property provides the basis for solving quadratic equations and simplifying radical expressions, tying back to the earlier concepts of radicals.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions

Topic

Rationals and Radicals

Description

Subtraction of Rational Expressions involves subtracting one rational expression from another, resulting in another rational expression. The example simplifies 1/(x + 1) - 1/(x - 1) into -2/(x2 - 1) by finding a common denominator and combining the terms. This term supports the topic by illustrating how operations on rational expressions, like subtraction, can be performed systematically.

Rational Functions and Equations
Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions (Spanish Audio) Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions (Spanish Audio) Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions (Spanish Audio)

Topic

Rationals and Radicals

Rational Functions and Equations
Video Definition 46--Rationals and Radicals--Vertical Asymptote Video Definition 46--Rationals and Radicals--Vertical Asymptote Video Definition 46--Rationals and Radicals--Vertical Asymptote

Topic

Rationals and Radicals

Description

A Vertical Asymptote is defined by the restricted values of x where the function approaches but does not touch. For example, in y = 1/(x - 2), the function is not defined at x = 2, resulting in a vertical asymptote at that point. This term relates to rational expressions by identifying points of discontinuity, which are critical in understanding the behavior of rational functions.

Rational Functions and Equations
Video Definition 46--Rationals and Radicals--Vertical Asymptote (Spanish Audio) Video Definition 46--Rationals and Radicals--Vertical Asymptote (Spanish Audio) Video Definition 46--Rationals and Radicals--Vertical Asymptote (Spanish Audio)

Topic

Rationals and Radicals

Description

A Vertical Asymptote is defined by the restricted values of x where the function approaches but does not touch. For example, in y = 1/(x - 2), the function is not defined at x = 2, resulting in a vertical asymptote at that point. This term relates to rational expressions by identifying points of discontinuity, which are critical in understanding the behavior of rational functions.

Rational Functions and Equations
Video Definition 47--Rationals and Radicals--Zero of a Rational Function Video Definition 47--Rationals and Radicals--Zero of a Rational Function Video Definition 47--Rationals and Radicals--Zero of a Rational Function

Topic

Rationals and Radicals

Description

The Zero of a Rational Function is the value of the input variable for which the rational function equals zero. For example, in f(x) = (x - 1)/(x + 1), the zero occurs at x = 1. This term highlights the connection between the numerator of a rational function and its roots, which are essential for solving equations involving rational expressions.

Rational Functions and Equations
Video Definition 47--Rationals and Radicals--Zero of a Rational Function (Spanish Audio) Video Definition 47--Rationals and Radicals--Zero of a Rational Function (Spanish Audio) Video Definition 47--Rationals and Radicals--Zero of a Rational Function (Spanish Audio)

Topic

Rationals and Radicals

Description

The Zero of a Rational Function is the value of the input variable for which the rational function equals zero. For example, in f(x) = (x - 1)/(x + 1), the zero occurs at x = 1. This term highlights the connection between the numerator of a rational function and its roots, which are essential for solving equations involving rational expressions.

Rational Functions and Equations
Video Definition 5--Rationals and Radicals--Cube Root Video Definition 5--Rationals and Radicals--Cube Root Video Definition 5--Rationals and Radicals--Cube Root

Topic

Rationals and Radicals

Description

The cube root of a number, when multiplied by itself three times, equals the given number. Examples include ∛27 = 3, ∛125 = 5, and ∛8 = 2. Cube roots are essential for solving equations involving cubic powers and for understanding radical expressions.

Understanding this video is essential for grasping the fundamentals of Rationals and Radicals. The mathematical concepts explored here form the basis for further exploration and application in related fields.

Radical Expressions
Video Definition 5--Rationals and Radicals--Cube Root (Spanish Audio) Video Definition 5--Rationals and Radicals--Cube Root (Spanish Audio) Video Definition 5--Rationals and Radicals--Cube Root (Spanish Audio)

Topic

Rationals and Radicals

Description

The cube root of a number, when multiplied by itself three times, equals the given number. Examples include ∛27 = 3, ∛125 = 5, and ∛8 = 2. Cube roots are essential for solving equations involving cubic powers and for understanding radical expressions.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Definition 6--Rationals and Radicals--Division of Rational Expressions Video Definition 6--Rationals and Radicals--Division of Rational Expressions Video Definition 6--Rationals and Radicals--Division of Rational Expressions

Topic

Rationals and Radicals

Description

Division of rational expressions involves dividing one rational expression by another, resulting in a new rational expression. Examples include 1 / (2x2) ÷ 1 / (3x) = 3 / 2x and 2 / (x + 1) ÷ (3 / (x - 1)) = 2(x - 1) / 3(x + 1). This operation is crucial for manipulating and simplifying rational expressions in algebra.

Rational Functions and Equations
Video Definition 6--Rationals and Radicals--Division of Rational Expressions (Spanish Audio) Video Definition 6--Rationals and Radicals--Division of Rational Expressions (Spanish Audio) Video Definition 6--Rationals and Radicals--Division of Rational Expressions (Spanish Audio)

Topic

Rationals and Radicals

Description

Division of rational expressions involves dividing one rational expression by another, resulting in a new rational expression. Examples include 1 / (2x2) ÷ 1 / (3x) = 3 / 2x and 2 / (x + 1) ÷ (3 / (x - 1)) = 2(x - 1) / 3(x + 1). This operation is crucial for manipulating and simplifying rational expressions in algebra.

Rational Functions and Equations
Video Definition 7--Rationals and Radicals--Extraneous Solution Video Definition 7--Rationals and Radicals--Extraneous Solution Video Definition 7--Rationals and Radicals--Extraneous Solution

Topic

Rationals and Radicals

Description

An extraneous solution is a false solution discarded during the solving process. For example, solving √(x + 1) = x - 5 gives x = 3 or x = 8, but x = 3 is extraneous as it does not satisfy the original equation. This concept highlights the need to verify solutions in equations involving radicals or rational expressions.

Rational Functions and Equations
Video Definition 7--Rationals and Radicals--Extraneous Solution (Spanish Audio) Video Definition 7--Rationals and Radicals--Extraneous Solution (Spanish Audio) Video Definition 7--Rationals and Radicals--Extraneous Solution (Spanish Audio)

Topic

Rationals and Radicals

Description

An extraneous solution is a false solution discarded during the solving process. For example, solving √(x + 1) = x - 5 gives x = 3 or x = 8, but x = 3 is extraneous as it does not satisfy the original equation. This concept highlights the need to verify solutions in equations involving radicals or rational expressions.

Rational Functions and Equations
Video Definition 8--Rationals and Radicals--Factoring a Radical Video Definition 8--Rationals and Radicals--Factoring a Radical Video Definition 8--Rationals and Radicals--Factoring a Radical

Topic

Rationals and Radicals

Description

Factoring a radical expression involves extracting whole number factors. For example, √(36x2) = 6x or solving x = (-6 ± √(36 - 16)) / 4, which simplifies to -3 ± √5 / 2. Factoring radicals is a key step in simplifying expressions and solving equations with square roots.

Radical Functions and Equations
Video Definition 8--Rationals and Radicals--Factoring a Radical (Spanish Audio) Video Definition 8--Rationals and Radicals--Factoring a Radical (Spanish Audio) Video Definition 8--Rationals and Radicals--Factoring a Radical (Spanish Audio)

Topic

Rationals and Radicals

Description

Factoring a radical expression involves extracting whole number factors. For example, √36x2 = 6x or solving x = (-6 ± √(36 - 16)) / 4, which simplifies to -3 ± √5 / 2. Factoring radicals is a key step in simplifying expressions and solving equations with square roots.

This video includes Spanish audio and can be used with multilingual learners.

Radical Functions and Equations
Video Definition 9--Rationals and Radicals--Fourth Root Video Definition 9--Rationals and Radicals--Fourth Root Video Definition 9--Rationals and Radicals--Fourth Root

Topic

Rationals and Radicals

Description

The fourth root of a number, when multiplied by itself four times, equals the given number. Examples include ∜16 = 2 and ∜81 = 3. Fourth roots extend the concept of radicals to higher powers, useful in algebraic and geometric contexts.

Understanding this video is essential for grasping the fundamentals of Rationals and Radicals. The mathematical concepts explored here form the basis for further exploration and application in related fields.

Radical Expressions
Video Definition 9--Rationals and Radicals--Fourth Root (Spanish Audio) Video Definition 9--Rationals and Radicals--Fourth Root (Spanish Audio) Video Definition 9--Rationals and Radicals--Fourth Root (Spanish Audio)

Topic

Rationals and Radicals

Description

The fourth root of a number, when multiplied by itself four times, equals the given number. Examples include ∜16 = 2 and ∜81 = 3. Fourth roots extend the concept of radicals to higher powers, useful in algebraic and geometric contexts.

This video includes Spanish audio and can be used with multilingual learners.

Radical Expressions
Video Transcript: Algebra Applications: Rational Functions Video Transcript: Algebra Applications: Rational Functions Video Transcript: Algebra Applications: Rational Functions

This is the transcript for the video of same title. Video contents: In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of rational functions. Such disparate phenomena as submarines, photography, and the appearance of certain organisms can be explained through rational function models.

Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Applications: Rational Functions, Segment 1: Submarines Video Transcript: Algebra Applications: Rational Functions, Segment 1: Submarines Video Transcript: Algebra Applications: Rational Functions, Segment 1: Submarines

This is the transcript for the video of same title. Video contents: In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine.

Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Applications: Rational Functions, Segment 2: Biology Video Transcript: Algebra Applications: Rational Functions, Segment 2: Biology Video Transcript: Algebra Applications: Rational Functions, Segment 2: Biology

This is the transcript for the video of same title. Video contents: All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

Rational Expressions and Rational Functions and Equations