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Mastering Simplified Radical Form in Math

Learn to simplify radical expressions by factoring out perfect squares, combining like terms, and eliminating fractions. Understand the Multiplication and Division Properties of Square Roots to rationalize denominators effectively.

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Mastering Simplified Radical Form in Math

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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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