Solve 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 and simplify.

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What does it mean if you get a negative value when isolating a radical?

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It indicates that there is no solution, as the square root (or any even root) cannot be negative.

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What is the importance of checking your solution in radical equations?

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Checking ensures that the solution does not produce extraneous results, which can occur when squaring both sides of an equation.

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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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What is the general approach to solving radical equations?

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1. Isolate the radical. 2. Raise both sides to the appropriate power. 3. Solve the resulting equation. 4. Check for extraneous solutions.