11-8 Radical Radial Expressions Warm Up Lesson Presentation Lesson Quiz 1
Warm Up Simplify each expression. 1. 2. 3. 4.
Objectives Multiply and divide radical expressions. Rationalize denominators.
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. Factor 4 using a perfect-square factor. Product Property of Square Roots. 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 25 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. Factor 14 using a perfect-square factor. Product Property of Square Roots. Take the square root. Simplify.
Example 2A: Using the Distributive Property Multiply. Write each product in simplest form. 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.
Example 2B: Using the Distributive Property Multiply. Write the product in simplest form. Distribute Product Property of Square Roots. Simplify the radicands. Simplify.
Check It Out! Example 2a Multiply. Write the product in simplest form. 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.
Check It Out! Example 2b Multiply. Write the product in simplest form. Distribute Product Property of Square Roots. Simplify the radicand. Simplify.
Check It Out! Example 2c Multiply. Write the product in simplest form. Distribute Product Property of Square Roots. Simplify the radicand. Simplify.
Check It Out! Example 2d Multiply. Write each product in simplest form. Distribute Product Property of Square Roots. Simplify the radicand. Simplify.
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.
Remember! First terms Outer terms Inner terms Last terms See Lesson 7-7.
= 20 + 3
Example 3A: 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.
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 perfectsquare radicand in the denominator. Product Property of Square Roots. Simplify the denominator.
Example 4B: Rationalizing the Denominator Simplify the quotient. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Simplify the square root in denominator.
Check It Out! Example 4a Simplify the quotient. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Simplify the square root in denominator.
Check It Out! Example 4b Simplify the quotient. Multiply by a form of 1 to get a perfectsquare radicand in the denominator. Simplify the square root in denominator.
Check It Out! Example 4c 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.
Lesson Quiz Multiply. Write each product in simplest form. 1. 3. 5. 2. 4. 6. 7. Simplify each quotient. 8. 9.