11 4 Multiplying and Dividing Radical Expressions Preview

11 -4 Multiplying and Dividing Radical Expressions Warm Up Simplify each expression. 1. 2.

11 -4 Multiplying and Dividing Radical Expressions California Standards Extension of 2. 0 Students

11 -4 Multiplying and Dividing Radical Expressions You can use the Product and Quotient

11 -4 Multiplying and Dividing Radical Expressions Additional Example 1 A: Multiplying Square Roots

11 -4 Multiplying and Dividing Radical Expressions Additional Example 1 B: Multiplying Square Roots

11 -4 Multiplying and Dividing Radical Expressions Additional Example 1 C: Multiplying Square Roots

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 1 a Multiply.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 1 b Multiply.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 1 c Multiply.

11 -4 Multiplying and Dividing Radical Expressions Additional Example 2 A: Using the Distributive

11 -4 Multiplying and Dividing Radical Expressions Additional Example 2 B: Using the Distributive

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 2 a Multiply.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 2 b Multiply.

11 -4 Multiplying and Dividing Radical Expressions In Chapter 7, you multiplied binomials by

11 -4 Multiplying and Dividing Radical Expressions Remember! First terms Outer terms Inner terms

11 -4 Multiplying and Dividing Radical Expressions = 20 +3

11 -4 Multiplying and Dividing Radical Expressions Additional Example 3 A: Multiplying Sums and

11 -4 Multiplying and Dividing Radical Expressions Additional Example 3 B: Multiplying Sums and

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 3 a Multiply.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 3 b Multiply.

11 -4 Multiplying and Dividing Radical Expressions A quotient with a square root in

11 -4 Multiplying and Dividing Radical Expressions Additional Example 4 A: Rationalizing the Denominator

11 -4 Multiplying and Dividing Radical Expressions Additional Example 4 B: Rationalizing the Denominator

11 -4 Multiplying and Dividing Radical Expressions Helpful Hint Use the square root in

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 4 a Simplify

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 4 b Simplify

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 4 c Simplify

11 -4 Multiplying and Dividing Radical Expressions Lesson Quiz Multiply. Write each product in

Slides: 29

Download presentation

11 -4 Multiplying and Dividing Radical Expressions Preview Warm Up California Standards Lesson Presentation

11 -4 Multiplying and Dividing Radical Expressions Warm Up Simplify each expression. 1. 2. 3. 4.

11 -4 Multiplying and Dividing Radical Expressions California Standards Extension of 2. 0 Students understand use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand use the rules of exponents.

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 1 A: 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 1 B: Multiplying Square Roots Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Expand the expression. Commutative Property of Multiplication Product Property of Square Roots. Simplify the radicand. Simplify the square root. Multiply.

11 -4 Multiplying and Dividing Radical Expressions Additional Example 1 C: Multiplying Square Roots Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Factor 12 using a perfect-square factor. Simplify the radicand. Product Property of Square Roots Simplify.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 1 a Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Product Property of Square Roots Multiply the factors in the radicand. Factor 50 using a perfect-square factor. Product Property of Square Roots

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 1 b Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Expand the expression. Commutative Property of Multiplication Product Property of Square Roots Simplify the radicand. Simplify the square root. Multiply.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 1 c Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Factor 14 m. Product Property of Square Roots Simplify.

11 -4 Multiplying and Dividing Radical Expressions Additional Example 2 A: Using the Distributive Property Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute 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.

11 -4 Multiplying and Dividing Radical Expressions Additional Example 2 B: Using the Distributive Property Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute Product Property of Square Roots Simplify the radicands. Simplify.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 2 a Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute 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.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 2 b Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute Product Property of Square Roots Factor 50 using a perfect-square factor. Simplify.

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 Remember! First terms Outer terms Inner terms Last terms See Lesson 7 -8.

11 -4 Multiplying and Dividing Radical Expressions = 20 +3

11 -4 Multiplying and Dividing Radical Expressions Additional Example 3 A: Multiplying Sums and Differences of Radicals Multiply. Write the product in simplest form. Use the FOIL method. Simplify by combining like terms. Simplify the radicand. Simplify.

11 -4 Multiplying and Dividing Radical Expressions Additional Example 3 B: 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 3 a 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 3 b 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 4 A: Rationalizing the Denominator Simplify the quotient. All variables represent nonnegative numbers. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Product Property of Square Roots Simplify the denominator.

11 -4 Multiplying and Dividing Radical Expressions Additional Example 4 B: Rationalizing the Denominator Simplify the quotient. All variables represent nonnegative numbers. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Simplify the square root in denominator.

11 -4 Multiplying and Dividing Radical Expressions Helpful Hint Use the square root in the denominator to find the appropriate form of 1 for multiplication.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 4 a Simplify the quotient. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Simplify the square root in denominator.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 4 b Simplify the quotient. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Simplify the square root in denominator.

11 -4 Multiplying and Dividing Radical Expressions Check It Out! Example 4 c Simplify the quotient. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Simplify the square root in denominator. Factor and simplify the square root in the numerator.

11 -4 Multiplying and Dividing Radical Expressions Lesson Quiz Multiply. Write each product in simplest form. All variables represent nonnegative numbers. 1. 2. 3. 4. 5. 6. 7. Simplify each quotient. All variables represent nonnegative numbers. 8. 9.