 # Chapter 7 – Powers, Roots, and Radicals

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Chapter 7 – Powers, Roots, and Radicals

Today we will be: Solving equations that contain radicals or rational exponents

Radical equation – an equation that contains radicals with the variable in the radicand. √(x + 6) = 5

Isolate the radical on one side of the equation, if needed. Raise each side of the equation to the same power to eliminate the radical. Solve the resulting equation using techniques that you learned in previous chapters. Check your solution.

Example 1 Solve 3√y – 4 = 0

Example 2 2√(x + 12) – 3 = 5.

To solve an equation with two radicals, first rewrite the equation so that each side has only one radical. Then raise each side of the equation to the same power.

Example 3 Solve √3x - √(x + 6) = 0.

Extraneous solution – an apparent solution that does not make the original equation true. Raising each side of an equation to the same power can lead to solutions that do not make the original equation true. You must check each apparent solution in the original equation Any solution that does not satisfy the original equation is extraneous

Example 4 Solve x = √(x + 12). Check for extraneous solutions.

When an equation contains a power with a rational exponent, you solve the equation the same way you would solve a radical equation. Isolate the power on one side of the equation Raise each side of the equation to the reciprocal of the rational exponent Solve for the variable