Algebra 2 unit 6.2

UNIT 6.2 MULTIPLYING AND UNIT 6.2 MULTIPLYING AND DIVIDING RADICAL DIVIDING RADICAL

EXPRESSIONSEXPRESSIONS

Warm Up

Simplify each expression.

1.

2.

3.

4.

Multiply and divide radical expressions. Rationalize denominators.

Objectives

You can use the Product and Quotient Properties of square roots you have already learned to multiply and divide expressions containing square roots.

Example 1A: Multiplying Square Roots

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Multiply the factors in the radicand.

Factor 16 using a perfect-square factor.

Product Property of Square Roots

Simplify.

Example 1B: Multiplying Square Roots

Multiply. Write the product in simplest form.

Expand the expression.

Commutative Property of Multiplication.

Product Property of Square Roots.

Simplify the radicand.

Simplify the Square Root.

Multiply.

Example 1C: Multiplying Square Roots

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Factor 12 using a perfect-square factor.

Take the square root..

Simplify.

Check It Out! Example 1a

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Multiply the factors in the radicand.

Factor 50 using a perfect-square factor.

Product Property of Square Roots

Simplify.

Check It Out! Example 1b

Multiply. Write the product in simplest form.

Expand the expression.

Commutative Property of Multiplication.

Product Property of Square Roots.

Simplify the radicand.

Simplify the Square Root.

Multiply.

Check It Out! Example 1c

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Factor 14 using a perfect-square factor.

Take the square root.

Simplify.

Example 2A: Using the Distributive Property

Multiply. Write each product in simplest form.

Product Property of Square Roots.

Multiply the factors in the second radicand.

Factor 24 using a perfect-square factor.

Product Property of Square Roots.

Simplify.

Distribute

Example 2B: Using the Distributive Property

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Distribute

Simplify the radicands.

Simplify.

Check It Out! Example 2a

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Multiply the factors in the first radicand.

Factor 48 using a perfect-square factor.

Product Property of Square Roots.

Simplify.

Distribute

Check It Out! Example 2b

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Simplify the radicand.

Simplify.

Distribute

Check It Out! Example 2c

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Simplify the radicand.

Simplify.

Distribute

Check It Out! Example 2d

Multiply. Write each product in simplest form.

Product Property of Square Roots.

Simplify the radicand.

Simplify.

Distribute

In Chapter 7, you learned to multiply binomials by using the FOIL method. The same method can be used to multiply square-root expressions that contain two terms.

First terms

Outer terms

Inner terms

Last terms

See Lesson 7-7.

Remember!

= 20 + 3

Example 3A: Multiplying Sums and Differences of Radicals

Multiply. Write the product in simplest form.

Use the FOIL method.

Simplify the radicand.

Simplify by combining like terms.

Simplify.

Example 3B: Multiplying Sums and Differences of Radicals

Multiply. Write the product in simplest form.

Expand the expression.

Use the FOIL method.

Simplify by combining like terms.

Check It Out! Example 3a

Multiply. Write the product in simplest form.

Use the FOIL method.

Simplify by combining like terms.

Check It Out! Example 3b

Multiply. Write the product in simplest form.

Expand the expression.

Use the FOIL method.

Simplify by combining like terms.

Check It Out! Example 3c

Multiply. Write the product in simplest form.

Expand the expression.

Use the FOIL method.

Simplify by combining like terms.

Check It Out! Example 3d

Multiply. Write the product in simplest form.

Use the FOIL method.

Simplify by combining like terms.

A quotient with a square root in the denominator is not simplified. To simplify these expressions, multiply by a form of 1 to get a perfect-square radicand in the denominator. This is called rationalizing the denominator.

Example 4A: Rationalizing the Denominator

Simplify the quotient.

Multiply by a form of 1 to get a perfect-square radicand in the denominator.

Product Property of Square Roots.

Simplify the denominator.

Example 4B: Rationalizing the Denominator

Simplify the quotient.

Simplify the square root in denominator.

Multiply by a form of 1 to get a perfect-square radicand in the denominator.

Check It Out! Example 4a

Simplify the quotient.

Simplify the square root in denominator.

Multiply by a form of 1 to get a perfect-square radicand in the denominator.

Check It Out! Example 4b

Simplify the quotient.

Simplify the square root in denominator.

Multiply by a form of 1 to get a perfect-square radicand in the denominator.

Check It Out! Example 4c

Simplify the quotient.

Simplify the square root in denominator.

Multiply by a form of 1 to get a perfect-square radicand in the denominator.

Factor and simplify the square root in the numerator.

Lesson Quiz

Multiply. Write each product in simplest form.

1.

3.

Simplify each quotient.

5.

8. 9.

2.

4.

6.

7.

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