11-4 Multiplying and Dividing Radical Expressions Warm Up Warm Up Lesson Presentatio n California Standar ds Preview Preview
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11-4 Multiplying and Dividing Radical Expressions
Warm UpWarm Up
Lesson Presentation
California Standards
PreviewPreview
11-4 Multiplying and Dividing Radical Expressions
Warm Up
Simplify each expression.
1.
2.
3.
4.
11-4 Multiplying and Dividing Radical Expressions
Extension of 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
California Standards
11-4 Multiplying and Dividing Radical Expressions
You can use the Product and Quotient Properties of square roots you have already learned to multiply and divide expressions containing square roots.
11-4 Multiplying and Dividing Radical Expressions
Additional Example 1A: Multiplying Square Roots
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
Product Property of Square Roots
Multiply the factors in the radicand.
Factor 16 using a perfect-square factor.
Product Property of Square Roots
Simplify.
11-4 Multiplying and Dividing Radical Expressions
Additional Example 1B: Multiplying Square Roots
Expand the expression.
Commutative Property of Multiplication
Product Property of Square Roots.
Simplify the radicand.
Simplify the square root.
Multiply.
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
Additional Example 1C: Multiplying Square Roots
Simplify the radicand.
Factor 12 using a perfect-square factor.
Product Property of Square Roots
Simplify.
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
Check It Out! Example 1a
Product Property of Square Roots
Multiply the factors in the radicand.
Factor 50 using a perfect-square factor.
Product Property of Square Roots
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
Check It Out! Example 1b
Expand the expression.
Commutative Property of Multiplication
Product Property of Square Roots
Simplify the radicand.
Simplify the square root.
Multiply.
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
Check It Out! Example 1c
Product Property of Square Roots
Factor 14m.
Product Property of Square Roots
Simplify.
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical ExpressionsAdditional Example 2A: Using the Distributive Property
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
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
Additional Example 2B: Using the Distributive Property
Product Property of Square Roots
Distribute
Simplify the radicands.
Simplify.
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical ExpressionsCheck It Out! Example 2a
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
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
Check It Out! Example 2b
Product Property of Square Roots
Factor 50 using a perfect-square factor.Simplify.
Distribute
Multiply. Write the product in simplest form. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
In Chapter 7, you multiplied binomials by using the FOIL method. The same method can be used to multiply square-root expressions that contain two terms.
11-4 Multiplying and Dividing Radical Expressions
First terms
Outer terms
Inner terms
Last terms
See Lesson 7-8.
Remember!
11-4 Multiplying and Dividing Radical Expressions
= 20 + 3
11-4 Multiplying and Dividing Radical Expressions
Additional 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.
11-4 Multiplying and Dividing Radical Expressions
Additional 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.
11-4 Multiplying and Dividing Radical Expressions
Check It Out! Example 3a
Multiply. Write the product in simplest form.
Expand the expression.
Use the FOIL method.
Simplify by combining like terms.
11-4 Multiplying and Dividing Radical Expressions
Check It Out! Example 3b
Multiply. Write the product in simplest form.
Use the FOIL method.
Simplify by combining like terms.
11-4 Multiplying and Dividing Radical 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.
11-4 Multiplying and Dividing Radical Expressions
Additional Example 4A: Rationalizing the Denominator
Simplify the quotient. All variables represent nonnegative numbers.
Multiply by a form of 1 to get a perfect-square radicand in the denominator.
Product Property of Square Roots
Simplify the denominator.
11-4 Multiplying and Dividing Radical Expressions
Additional Example 4B: Rationalizing the Denominator
Simplify the square root in denominator.
Multiply by a form of 1 to get a perfect-square radicand in the denominator.
Simplify the quotient. All variables represent nonnegative numbers.
11-4 Multiplying and Dividing Radical Expressions
Use the square root in the denominator to find the appropriate form of 1 for multiplication.
Helpful Hint
11-4 Multiplying and Dividing Radical 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.
11-4 Multiplying and Dividing Radical 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.
11-4 Multiplying and Dividing Radical ExpressionsCheck 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.
11-4 Multiplying and Dividing Radical ExpressionsLesson Quiz
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Multiply. Write each product in simplest form. All variables represent nonnegative numbers.
8. 9.
Simplify each quotient. All variables represent nonnegative numbers.
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