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**Simplify Radical Expressions**

What steps would you take in simplifying the following: √(3+92)

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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 expression’s 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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Multiplying Radicals * 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**

Combining Radicals + 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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To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

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