Solve Radical Equations

Front

What is a radical equation?

Back

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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Back

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

Front

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

Back

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

Front

What does it mean to check your solution in a radical equation?

Back

Checking your solution means substituting it back into the original equation to ensure it satisfies the equation.

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Back

x = 0.5.

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What is an extraneous solution?

Back

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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Back

Square both sides to get x = 25.

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What is the importance of the domain in radical equations?

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The domain is important because it defines the set of values for which the radical expression is defined (e.g., non-negative values for square roots).

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x = 46.