Rational Exponents and Solving Radical Equations Objective 1

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. The value of the denominator represents the index or root of the expression.

Examples

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

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

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 no

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

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

Let’s Try Some

Let’s Try Some

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

Can graphing calculators help? SURE! 1. 2. 3. 4. Input for Y 1 Input x-2 for Y 2 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?