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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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