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Simplified Radical Form

Simplified Radical Form. Objective: Describe simplified Radical Form Simplify radical expressions by a) Factoring out perfect squares b) Combine Like Terms. Vocabulary. Square Root : If a 2 = b, then a is the square root of b. Ex:. Most numbers have 2 square roots.

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Simplified Radical Form

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  1. Simplified Radical Form Objective: • Describe simplified Radical Form • Simplify radical expressions by a) Factoring out perfect squares b) Combine Like Terms

  2. Vocabulary Square Root: If a2 = b, then a is the square root of b. Ex: Most numbers have 2 square roots. Principal (positive)Negative To indicate both:

  3. Vocabulary Perfect Square: Numbers whose square roots are integers. Ex: Approximate vs. Exact Values for Irrational Numbers Square Roots of Negative Numbers

  4. Simplified Radical Form In order for a radical expression to be simplified, the following must be true. • The expression under the radical sign has no perfect square factors other than 1. • For sums and differences, like radical terms are combined • There are no fractions under the radical. • There are no radicals in the denominator of a fraction.

  5. Multiplication Property of Square Roots For any numbers a ≥ 0 and b ≥ 0, Ex:

  6. Using the Multiplication Property to Simplify Radical Expressions “Factor” Perfect Square factors out from under the radical. Simplify

  7. Simplified Radical Form (Continued) Objective: Simplify radical expressions by a) Eliminating Fractions from under the radical b) Rationalize the denominator

  8. Division Property of Square Roots For any numbers a ≥ 0 and b > 0, Ex:

  9. Simplify

  10. Rationalizing the Denominator* *Means to get rid of an irrational number in the denominator of a fraction To Rationalize the Denominator of a fraction, multiple the numerator and denominator by a radical that will create a perfect square under the radical of the denominator.

  11. Simplify

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