Simplify Radical Expressions

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What is a radical expression?

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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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To simplify radical expressions, factor the number under the radical into its prime factors and look for pairs of factors. For example, @@ ext{simplifying } 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 square root of 25?

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How do you simplify @@2 ext{ } oot{2}{50}@@?

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@@2 ext{ } oot{2}{50} = 2 ext{ } oot{2}{25 imes 2} = 2 ext{ } oot{2}{25} imes oot{2}{2} = 2 imes 5 imes oot{2}{2} = 10 oot{2}@@.

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What is the simplified form of @@ ext{ } oot{2}{200}@@?

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@@ ext{ } oot{2}{200} = ext{ } oot{2}{100 imes 2} = ext{ } oot{2}{100} imes ext{ } oot{2}{2} = 10 ext{ } oot{2}{2} = 10 ext{ } oot{2}@@.

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How do you simplify @@ ext{ } oot{2}{50x^4}@@?

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@@ ext{ } oot{2}{50x^4} = ext{ } oot{2}{25 imes 2} imes ext{ } oot{2}{x^4} = 5 ext{ } oot{2}{2} imes x^2 = 5x^2 ext{ } oot{2}{2}@@.

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What is the simplified form of @@3x ext{ } oot{2}{50x^2y}@@?

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@@3x ext{ } oot{2}{50x^2y} = 3x ext{ } oot{2}{25 imes 2} imes ext{ } oot{2}{x^2} imes ext{ } oot{2}{y} = 3x imes 5 ext{ } oot{2}{2} imes x imes ext{ } oot{2}{y} = 15x^2 ext{ } oot{2}{2y}@@.

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What is the value of @@-3 ext{ } oot{2}{25}@@?

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@@-3 ext{ } oot{2}{25} = -3 imes 5 = -15@@.

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What is the principle of simplifying radicals?

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The principle of simplifying radicals involves expressing the radical in its simplest form by factoring out perfect squares (or cubes, etc.) from under the radical.