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Rational Exponents and Solving Radical Equations

Rational Exponents and Solving Radical Equations. Objective 1:. You will be able to simplify expressions involving rational exponents. What is a Rational Exponent. Formal Definition of Rational Exponent. The value of the numerator represents the power of the radicand.

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Rational Exponents and Solving Radical Equations

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  1. Rational Exponents and Solving Radical Equations

  2. Objective 1: • You will be able to simplify expressions involving rational exponents.

  3. What is a Rational Exponent

  4. Formal Definition of Rational Exponent The value of the numerator represents the power of the radicand. The value of the denominator represents the index or root of the expression.

  5. Examples

  6. Now it’s your turn to practice • I Have, Who Has Activity

  7. Objective 2: • You will be able to solve radical and rational equations.

  8. What is a Radical Expression? • A Radical Expression is an equation that has a variable in a radicand or has a variable with a rational exponent. yes yes no

  9. EXAMPLE – Solving a Radical Equation 2 2 Square both sides to get rid of the square root ( )

  10. EXAMPLE 2 2 ( ) NO SOLUTION Since 16 doesn’t plug in as a solution. Note: You will get Extraneous Solutions from time to time – always do a quick check Let’s Double Check that this works

  11. Let’s Try Some

  12. Let’s Try Some

  13. RADICAL EQUATIONS ISOLATE RADICAL / RATIONAL RAISE BOTH SIDES TO RECIPROCAL POWER SOLVE FOR THE VARIABLE

  14. Can graphing calculators help? SURE! • Input for Y1 • Input x-2 for Y2 • Graph • Find the points of intersection One Solution at (4, 2) To see if this is extraneous or not, plug the x value back into the equation. Does it work?

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