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Then/Now I CAN simplify radical expressions by using the Product Property of Square Roots and the Quotient Property of Square Roots. Learning Target

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Concept 1 Radical Expression – an expression that contains a radical sign.

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

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A.A B.B C.C D.D Example 1 A. B. C.15 D.

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

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A.A B.B C.C D.D Example 2 A. B. C. D.35

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

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A.A B.B C.C D.D Example 3 A. B. C. D. nc

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Concept 2 Rationalize the Denominator - a process that involves multiplying the numerator and denominator by a factor that eliminates radicals in the denominator.

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

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Example 4 Product Property of Square Roots Solve the Test Item

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

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A.A B.B C.C D.D Example 4 A. B. C. D.

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Conjugates – binomials of the form: a b + c d and a b - c d

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

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A.A B.B C.C D.D Example 5 A. B. C. D.

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Rationalizing Numerators and Denominators of Radical Expressions 10.5 1.Rationalize denominators. 2.Rationalize denominators that have a sum or difference.

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