Radical Equations Flashcard

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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, leaving the radical alone on one side.

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The first step is to eliminate the fraction by multiplying both sides of the equation by the denominator.

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

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Squaring both sides of an equation can eliminate a square root, but it may introduce extraneous solutions that need to be checked.

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What does it mean if a radical equation has no solution?

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It means that there are no values for the variable that satisfy the equation, often due to taking the square root of a negative number.

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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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What is the importance of checking solutions in radical equations?

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Checking solutions is crucial to ensure that they satisfy the original equation and to identify any extraneous solutions.