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**Section P3 Radicals and Rational Exponents**

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Square Roots

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Examples Evaluate

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**Simplifying Expressions of the Form**

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**The Product Rule for Square Roots**

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**A square root is simplified when its radicand has no factors other than 1 that are perfect squares.**

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Examples Simplify:

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Examples Simplify:

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**The Quotient Rule for Square Roots**

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Examples Simplify:

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**Adding and Subtracting Square Roots**

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Two or more square roots can be combined using the distributive property provided that they have the same radicand. Such radicals are called like radicals.

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Example Add or Subtract as indicated:

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Example Add or Subtract as indicated:

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**Rationalizing Denominators**

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Rationalizing a denominator involves rewriting a radical expression as an equivalent expression in which the denominator no longer contains any radicals. If the denominator contains the square root of a natural number that is not a perfect square, multiply the numerator and the denominator by the smallest number that produces the square root of a perfect square in the denominator.

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**Let’s take a look two more examples:**

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Examples Rationalize the denominator:

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Examples Rationalize the denominator:

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Other Kinds of Roots

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Examples Simplify:

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**The Product and Quotient Rules for nth Roots**

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Example Simplify:

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Example Simplify:

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Rational Exponents

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Example Simplify:

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Example Simplify: Notice that the index reduces on this last problem.

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Simplify: (a) (b) (c) (d)

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Simplify: (a) (b) (c) (d)

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