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Simplifying Square Roots — Practice Problems

Test your skill at simplifying square roots. Each problem asks you to write a radical in simplest form by factoring out perfect squares. Click 'Show Answer' to see the step-by-step solution.

Quick Recap

To simplify n\sqrt{n}, find the largest perfect square factor of nn. If n=a2⋅bn = a^2 \cdot b, then n=ab\sqrt{n} = a\sqrt{b}. The expression is fully simplified when no perfect square (other than 1) divides the number under the radical.

Practice Problems

1
Simplify 50\sqrt{50}.
2
Simplify 72\sqrt{72}.
3
Simplify 200\sqrt{200}.
4
Simplify 48\sqrt{48}.
5
Simplify 98\sqrt{98}.
6
Simplify 180\sqrt{180}.
7
Simplify 128\sqrt{128}.
8
Simplify 3753\sqrt{75}.
9
Simplify 329\sqrt{\frac{32}{9}}.
10
Is 31\sqrt{31} already simplified? Explain.

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