Simplifying Radicals Worksheet With Answers - Section 6.2

Section 6.2 Simplifying Radicals

Multiplying Radicals

index must be the same

√ �� ∙ √ �� = √ ��

Example 1: If possible, multiply and then simplify.

a) √ 2 √ 5

b) √ 4 √ 16

c) 3 √ 6 (4 √ 6)

d) √ 2 √ 5

A radical expression is in simplified form if

1. There are no factors of the radicand that are

perfect squares under a square root, (4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, �� , �� , ….…)

no perfect cubes under a cube root, (8, 27, 64, 125, 216, �� , �� , ….)

no perfect fourths under a fourth root, (16, 81, 256, �� , �� , …..)

no perfect fifths under a fifth root, and so on. (32, 243, �� , ��

……)

2. There are no fractions under a radical symbol.

3. There are no radicals in the denominator.

Multiplying Radicals Rule in reverse

index must be the same

√ �� = √ �� ∙ √ ��

Example 2: Simplify the following radical expressions.

√ 50

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