Practice Square Roots in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The non-negative number bb such that b2=ab^2 = a, written a=b\sqrt{a} = b โ€” the inverse of squaring.

25\sqrt{25} asks: what number times itself equals 25? Answer: 5.

Showing a random 20 of 50 problems.

Example 1

medium
Evaluate 64โˆ’9\sqrt{64} - \sqrt{9}.

Example 2

medium
Evaluate 36ร—4\sqrt{36} \times \sqrt{4}.

Example 3

easy
Find 925\sqrt{\frac{9}{25}}.

Example 4

easy
Find 0.25\sqrt{0.25}.

Example 5

challenge
Between which two consecutive integers does 200\sqrt{200} lie, and which is it closer to?

Example 6

hard
Solve x=9\sqrt{x}=9 for xx.

Example 7

easy
Find 400\sqrt{400}.

Example 8

easy
Find 100\sqrt{100}.

Example 9

medium
Simplify 4964\sqrt{\frac{49}{64}}.

Example 10

easy
Find 14\sqrt{\frac{1}{4}}.

Example 11

easy
What does the principal square root convention say about 49\sqrt{49}?

Example 12

medium
A square has an area of 196196 cmยฒ. What is the side length of the square?

Example 13

medium
Rationalize the denominator: 63\dfrac{6}{\sqrt{3}}.

Example 14

easy
Find 49\sqrt{49}.

Example 15

medium
Estimate 30\sqrt{30} to one decimal place.

Example 16

medium
Evaluate 18โ‹…2\sqrt{18}\cdot\sqrt{2}.

Example 17

medium
Between which two consecutive integers does 60\sqrt{60} lie?

Example 18

hard
A square has diagonal 10210\sqrt{2}. Find its side length.

Example 19

challenge
Simplify 12+27\sqrt{12} + \sqrt{27} to the form aba\sqrt{b}.

Example 20

hard
Solve x+5=4\sqrt{x+5}=4 for xx.