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. contains , and since , you can pull the 6 out: . Think of it as freeing numbers that are 'ready' to leave the radical.
Showing a random 20 of 50 problems.
Example 1
hardSimplify .
Example 2
easySimplify .
Example 3
easySimplify .
Example 4
mediumSimplify assuming .
Example 5
easySimplify .
Example 6
mediumSimplify .
Example 7
challengeSimplify assuming .
Example 8
easyIs already in simplified radical form?
Example 9
mediumSimplify assuming .
Example 10
hardRationalize the denominator: .
Example 11
easySimplify .
Example 12
easySimplify .
Example 13
easySimplify assuming .
Example 14
mediumSimplify .
Example 15
easySimplify for .
Example 16
hardSimplify .
Example 17
mediumRationalize the denominator: .
Example 18
challengeSimplify .
Example 19
easySimplify .
Example 20
easySimplify assuming .