Practice Simplifying Radicals in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Simplifying a radical means rewriting it so no perfect-square factor remains under the root sign. For example, √50 = √(25·2) = 5√2. The result — called simplified radical form — has the smallest possible number under the radical.
Look inside the radical for perfect squares hiding as factors. \sqrt{72} contains 36 \times 2, and since \sqrt{36} = 6, you can pull the 6 out: \sqrt{72} = 6\sqrt{2}. Think of it as freeing numbers that are 'ready' to leave the radical.
Example 1
easySimplify \sqrt{72}.
Example 2
mediumSimplify \sqrt{50x^4y^3}.
Example 3
mediumSimplify \sqrt{200x^4y^3}.
Example 4
easySimplify \sqrt{48}.
Example 5
mediumSimplify \sqrt{\frac{18}{25}}.