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 variable in a radical equation?

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To isolate a variable, you can square both sides of the equation to eliminate the radical, then solve for the variable.

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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 an equation but does not satisfy the original equation.

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How do you check for extraneous solutions?

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Substitute the solution back into the original equation to see if it holds true.

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What do you do after isolating the radical in an equation?

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Square both sides of the equation to eliminate the radical.

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What happens if you square both sides of an equation incorrectly?

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You may introduce extraneous solutions that do not satisfy the original equation.

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