Simplifying 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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CCSS.8.NS.A.1

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To simplify radical expressions, factor the radicand into perfect squares (or cubes) and simplify accordingly. For example, @@ ext{simplifying } 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 product property of radicals?

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The product property states that @@ oot{n}{a} imes oot{n}{b} = oot{n}{a imes b}@@.

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What is the quotient property of radicals?

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The quotient property states that @@rac{ oot{n}{a}}{ oot{n}{b}} = oot{n}{rac{a}{b}}@@.

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How do you multiply two radical expressions?

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To multiply two radical expressions, use the product property: @@ oot{n}{a} imes oot{n}{b} = oot{n}{a imes b}@@ and simplify if possible.

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What is the definition of a perfect square?

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A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16 are perfect squares.

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CCSS.6.EE.A.1

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CCSS.7.NS.A.2D

CCSS.8.NS.A.1

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@@x^{rac{1}{n}} = oot{n}{x}@@.

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CCSS.HSN.RN.A.2

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What is the simplified form of @@ oot{2}{x^4}@@?

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@@ oot{2}{x^4} = x^2 oot{2}{1} = x^2@@.