holt algebra 1 11-8 multiplying and dividing radical expressions 11-8 multiplying and dividing...
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Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions11-8 Multiplying and Dividing
Radial Expressions
Holt Algebra 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Warm Up
Simplify each expression.
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4.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Multiply and divide radical expressions. Rationalize denominators.
Objectives
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
You can use the Product and Quotient Properties of square roots you have already learned to multiply and divide expressions containing square roots.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical ExpressionsExample 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
Holt Algebra 1
11-8 Multiplying and DividingRadical ExpressionsExample 2B: Using the Distributive Property
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Distribute
Simplify the radicands.
Simplify.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Check It Out! Example 2b
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Distribute
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Check It Out! Example 2c
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Distribute
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Check It Out! Example 2d
Multiply. Write each product in simplest form.
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Distribute
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
First terms
Outer terms
Inner terms
Last terms
See Lesson 7-7.
Remember!
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
= 20 + 3
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Check It Out! Example 3a
Multiply. Write the product in simplest form.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Check It Out! Example 3b
Multiply. Write the product in simplest form.
Expand the expression.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Check It Out! Example 3c
Multiply. Write the product in simplest form.
Expand the expression.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Check It Out! Example 3d
Multiply. Write the product in simplest form.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical ExpressionsExample 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.
Holt Algebra 1
11-8 Multiplying and DividingRadical ExpressionsExample 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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
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.
Holt Algebra 1
11-8 Multiplying and DividingRadical Expressions
Lesson Quiz
Multiply. Write each product in simplest form.
1.
3.
Simplify each quotient.
5.
8. 9.
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6.
7.