2. Radical Equations An equation in which the variable appears under a radical sign is called a radical equation. Isolate the radical Square both sides Solve the equation Check your answer Reject

3. Solving Radical Equations Graphically Enter each equation in the Y= window. Press GRAPH Press 2ndCALC5 (intersect) Move the curser until it is on the curve. Press ENTER The calculator calculates the point of intersection.

4. Fractional Equations A fractional equation is an equation in which the variable appears in the denominator of one or more fractions. To solve a fractional equation, eliminate the denominators by multiplying everything by the LCD of all the denominators. LCD = 10x Multiply by the LCD Cancel all denominators Solve the equation LCD = (8x)(x + 3)

5. More Fractional Equations Factor in order to find the LCD. LCD = (x + 2)(x - 2) Don’t forget to check for extraneous roots. If x = –2, then one of the fractions would be undefined. Therefore, -2 is an extraneous root. Reject That was easy

6. Radical vs Exponential Form All radicals can be written in exponential form. All exponents can be written in radical form. 4 3 52

7. Equations with Rational Exponents That doesn’t sound easy. Don’t worry. You’ll be pushing the easy button in just a few minutes. An equation with a rational exponent is an equation in which the variable is raised to an exponent that is a fraction. To solve an equation with a rational exponent, raise both sides to the reciprocal power of the variable in order to transform the exponent of the variable to 1.

8. Solving Equations with Rational Exponents Isolate the variable Raise both sides to the reciprocal of the exponent of the variable. Simplify the equation.

9. Rationalizing Denominators In order for a fraction to have a rational denominator, there cannot be a radical in the denominator. The process of rewriting the fraction in an equivalent form without a radical in the denominator is called Rationalizing the Denominator. Since there is a radical in the denominator, we must rationalize the denominator. Multiplying the radical by itself will remove it from the denominator. The new fraction is an equivalent form of the original fraction. They are Sam Ting! Let’s try one more.

10. Multiplying by the Conjugate Pair Conjugate Pairs are two binomial expressions that are the same with the exception of the sign in the middle. and are Conjugate Pairs. To rationalize the denominator of a fraction that has a binomial radical expression, you must multiply by the Conjugate Pair.

11. Radical Equation Word Problem The number of seconds in the period of a pendulum is the length of time required for the pendulum to make one complete swing back and forth. The formula gives the period, T, for a pendulum of length L in feet. If Todd wants to build a grandfather clock with a pendulum that swings back and forth every 2 seconds, how long, to the nearest tenth of a foot, should he make the pendulum? L is the variable and T = 2.