Simplify Radical Expressions

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Simplify Radical Expressions
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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.

4
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 1Use the product property of radicals

• Simplify the expression.

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Example 2Multiply radicals

• Simplify the expression.

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Example 3Use 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 4Rationalize the denominator
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Example 5Add and Subtract Radicals
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Guided Practice for Examples 4 5Add 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!