Solving Radical Equations

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What is a radical equation?

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A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

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How do you isolate a radical in an equation?

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To isolate a radical, you can move all other terms to the opposite side of the equation.

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Subtract 3 from both sides to isolate the radical: @@ \sqrt{n} = 0@@.

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Square both sides to eliminate the square root.

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What does it mean to check your solution in radical equations?

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It means substituting the solution back into the original equation to verify that both sides are equal.

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What is the importance of squaring both sides of an equation?

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Squaring both sides helps eliminate the radical, but it can introduce extraneous solutions that must be checked.

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What is an extraneous solution?

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An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation.

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