Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4

Including Rationalizing The Denominators

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.

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.

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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.

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Multiplying Square Roots

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Factor 4 using a perfect-square factor.

Take the square root..

Simplify.

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Multiply. Write the product in simplest form.

Product Property of Square Roots.

Multiply the factors in the radicand.

Factor 25 using a perfect-square factor.

Product Property of Square Roots

Simplify.

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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.

Try This!

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Factor 14 using a perfect-square factor.

Take the square root.

Simplify.

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

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Using the Distributive Property

Multiply. Write the product in simplest form.

Product Property of Square Roots.

Distribute

Simplify the radicands.

Simplify.

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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

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Multiply. Write the product in simplest form.

Product Property of Square Roots.

Simplify the radicand.

Simplify.

Distribute

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Multiply. Write the product in simplest form.

Product Property of Square Roots.

Simplify the radicand.

Simplify.

Distribute

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Multiply. Write each product in simplest form.

Product Property of Square Roots.

Simplify the radicand.

Simplify.

Distribute

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.

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.

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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.

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Simplify the quotient.

Simplify the square root in denominator.

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

Try This!

Simplify the quotient.

Simplify the square root in denominator.

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

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Try This!

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.

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Lesson Quiz

Multiply. Write each product in simplest form.

1.

3.

Simplify each quotient.

5.

7. 8.

2.

4.

6.