6.5C Solving Radical and Rational Exponent Equations

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What is a radical equation?

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An equation that involves a variable within a radical (square root, cube root, etc.).

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How do you solve a radical equation?

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Isolate the radical on one side, then square both sides to eliminate the radical, and solve the resulting equation.

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What is an extraneous solution?

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A solution that emerges from the process of solving an equation but does not satisfy the original equation.

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What is a rational exponent?

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An exponent that can be expressed as a fraction, where the numerator is the power and the denominator is the root.

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How do you convert a radical expression to a rational exponent?

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Use the formula @@ oot[n]{x} = x^{rac{1}{n}}@@.

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Multiply both sides by 3 to eliminate the fraction.

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What does it mean to check for extraneous solutions?

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Substituting the found solutions back into the original equation to verify if they hold true.

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