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 expression by extracting perfect square factors from under the radical sign so that no perfect square (other than 1) remains 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

easy
Simplify \sqrt{72}.

Example 2

medium
Simplify \sqrt{50x^4y^3}.

Example 3

medium
Simplify \sqrt{200x^4y^3}.

Example 4

easy
Simplify \sqrt{48}.

Example 5

medium
Simplify \sqrt{\frac{18}{25}}.