4.3 - Operations With 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 (for square roots) or groups (for cube roots) to simplify.

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What is the square root of 20?

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The square root of 20 can be simplified to @@2 ext{ } imes ext{ } oot{2}{5}@@.

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Simplify @@ ext{ } oot{2}{72}@@.

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@@ ext{ } oot{2}{72} = 6 ext{ } imes ext{ } oot{2}{2} = 6 ext{ } imes ext{ } oot{2}{2} = 6 ext{ } imes ext{ }2 = 12@@.

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What is the product of two square roots?

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The product of two square roots can be expressed as @@ oot{2}{a} imes oot{2}{b} = oot{2}{a imes b}@@.

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How do you add radical expressions?

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To add radical expressions, they must have the same index and radicand. For example, @@ oot{2}{a} + oot{2}{a} = 2 oot{2}{a}@@.

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What is the simplified form of @@ oot{2}{50}@@?

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@@ oot{2}{50} = 5 oot{2}{2}@@.

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What is the difference between rational and irrational numbers?

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Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction (e.g., @@ oot{2}@@ is irrational).

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How do you multiply radical expressions?

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To multiply radical expressions, multiply the numbers under the radicals and then simplify if possible. For example, @@ oot{2}{a} imes oot{2}{b} = oot{2}{ab}@@.

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