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Then/Now You simplified radicals. Simplify radical expressions by using the Product Property of Square Roots. Simplify radical expressions by using the Quotient Property of Square Roots.

Concept 1 In short: 1)Numbers under a root symbol can multiply with other numbers under the same type of root symbol. 2)Numbers under a root symbol can be broken up into the product of roots of the individual numbers.

Example 1 Simplify Square Roots Prime factorization of 52 Answer: = 2 ● Simplify. Product Property of Square Roots

Example 1 A. B. C.15 D.

Example 2 Multiply Square Roots Product Property Answer:4 = 2 ● 2 ● Simplify.

Example 2 A. B. C. D.35

7-1: Roots and Radical Expressions A weird quirk about roots –Notice that if x = 5, –But when x = -5, There needs to be some way to handle this situation –So if, at any time: Both the root and exponent underneath a radical are even And the output exponent is odd –The variable must be protected inside absolute value signs –Even → Even → Odd? Use Absolute Value Signs

Example 3 Simplify a Square Root with Variables Prime factorization Product Property Simplify. Answer:

Example 3 A. B. C. D.

Then/Now Assignment Page 631 Problems 17 – 33, odd exercises

Concept 2

Example 4 Which expression is equivalent to ? AC BDAC BD Read the Test Item The radical expression needs to be simplified.

Example 4 Product Property of Square Roots Solve the Test Item

Example 4 Prime factorization Simplify. Answer: The correct choice is D.

Example 4 A. B. C. D.

Example 5 Use Conjugates to Rationalize a Denominator (a – b)(a + b) = a 2 – b 2 Simplify.

Example 5 A. B. C. D.

Then/Now Assignment Page 632 Problems 37 – 47, odd exercises