Adding, Subtracting, and Multiplying Radicals

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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 (∛). For example, √4 is a radical that represents the number 2.

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CCSS.8.NS.A.1

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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 perfect squares (or cubes) to simplify. For example, √8 = √(4*2) = 2√2.

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What is the product of two square roots?

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The product of two square roots can be simplified using the property: √a × √b = √(a*b). For example, √5 × √10 = √(5*10) = √50 = 5√2.

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How do you add or subtract radical expressions?

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To add or subtract radical expressions, they must have the same index and radicand. For example, 2√3 + 3√3 = 5√3, but 2√2 + 3√3 cannot be combined.

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Tags

CCSS.HSN.RN.A.2

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What is the cube root of 27?

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The cube root of 27 is 3, since 3 × 3 × 3 = 27.

Tags

CCSS.8.EE.A.2

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How do you multiply a radical by a whole number?

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To multiply a radical by a whole number, simply multiply the whole number by the coefficient of the radical. For example, 3√5 = 3 * √5.

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