Simplify Square Roots worksheet for math practice.

Let’s simplify each square root step by step. We’ll look for perfect squares that divide into the number under the square root, then pull them out.

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√8
8 = 4 × 2 → √(4×2) = √4 × 2 = 2√2

√45
45 = 9 × 5 → √(9×5) = √9 × √5 = 3√5

√18
18 = 9 × 2 → √(9×2) = √9 × √2 = 3√2

√32
32 = 16 × 2 → √(16×2) = √16 × √2 = 4√2

√27
27 = 9 × 3 → √(9×3) = √9 × 3 = 3√3

√49
49 is a perfect square → √49 = 7

√28
28 = 4 × 7 → √(4×7) = √4 × √7 = 2√7

√128
128 = 64 × 2 → √(64×2) = √64 × √2 = 8√2

√75
75 = 25 × 3 → √(25×3) = √25 × √3 = 5√3

√96
96 = 16 × 6 → √(16×6) = √16 × √6 = 4√6

*(Note: 6 can’t be simplified further since it has no perfect square factors other than 1.)*

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Final Answer:
√8 = 2√2
√45 = 3√5
√18 = 3√2
√32 = 4√2
√27 = 3√3
√49 = 7
√28 = 2√7
√128 = 8√2
√75 = 5√3
√96 = 4√6