Simplifying Radicals & Radical Equations

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What is a radical?

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A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

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How do you simplify a radical expression?

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To simplify a radical expression, factor the number under the radical into its prime factors and look for pairs (for square roots) or triplets (for cube roots) to simplify.

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What is the square root of 45?

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What does it mean for a radical equation to have no solution?

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A radical equation has no solution when the radical is isolated and equal to a negative number.

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How do you multiply two radical expressions?

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To multiply two radical expressions, multiply the numbers outside the radicals and the numbers inside the radicals separately.

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What is the principle of squaring both sides of a radical equation?

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Squaring both sides of a radical equation can eliminate the radical, but it may introduce extraneous solutions.

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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.