Simplifying and Multiplying Radical Expressions

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

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Front

What is the product of two square roots?

Back

The product of two square roots can be simplified using the property: @@ ext{ } oot{2}{a} imes oot{2}{b} = oot{2}{a imes b}@@.

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Simplify @@ ext{ } oot{2}{8}@@.

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@@ ext{ } oot{2}{8} = oot{2}{4 imes 2} = oot{2}{4} imes oot{2}{2} = 2 oot{2}@@.

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What is the result of @@ ext{ } oot{2}{x^2}@@?

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@@ ext{ } oot{2}{x^2} = x@@, assuming x is non-negative.

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How do you multiply @@ ext{ } oot{2}{a} imes ext{ } oot{2}{b}@@?

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@@ ext{ } oot{2}{a} imes ext{ } oot{2}{b} = ext{ } oot{2}{ab}@@.

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What is the simplified form of @@ ext{ } oot{2}{18}@@?

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@@ ext{ } oot{2}{18} = oot{2}{9 imes 2} = 3 oot{2}@@.

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What is the result of multiplying a negative radical by a positive radical?

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The result will be negative. For example, @@-2 oot{3} imes 3 oot{2} = -6 oot{6}@@.

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How do you simplify @@ ext{ } oot{2}{x^4}@@?

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@@ ext{ } oot{2}{x^4} = x^2@@.

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What is the product of @@ ext{ } oot{2}{5} imes ext{ } oot{2}{5}@@?

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@@ ext{ } oot{2}{5} imes ext{ } oot{2}{5} = 5@@.