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Simplify Radical Expressions What steps would you take in simplifying the following: (3+9 2 )

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EQs… How do we simplify algebraic and numeric expressions involving square root? How do we perform operations with square roots?

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Vocabulary Simplest Form – A radical expression is in simplest form if no perfect square factors other than 1 are in the radicand, no fractions are in the radicand, and no radicals appear in the denominator of the fraction. Rationalizing the Denominator – The process of eliminating a radical from an expressions denominator.

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Vocabulary Radical Conjugates – Product Property of Radicals – States that the square root of a product equals the product of the square roots of the factors. Quotient Property of Radicals – States that the square roots of a quotient equals the quotient of the square roots of the numerator and denominator.

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Example 1 Use the product property of radicals Simplify the expression.

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* To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

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Multiply and then simplify

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Example 2 Multiply radicals Simplify the expression.

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Example 3 Use the quotient property of radicals Simplify the expression.

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Guided Practice for Examples 1, 2, & 3 Simplify the expression.

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Guided Practice for Examples 1, 2, & 3 Simplify the expression.

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Example 4 Rationalize the denominator

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+ To combine radicals: combine the coefficients of like radicals

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Simplify each expression

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Simplify each expression: Simplify each radical first and then combine.

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Example 5 Add and Subtract Radicals

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Guided Practice for Examples 4 & 5 Add and Subtract Radicals

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Joke of the Day… Why was the math book crying?

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It had too many problems!

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