Perfect square
√144 = 12 because 12 × 12 = 144. The √ sign asks for the zero-or-positive answer.
Find a square root
Square root calculator
Enter 0 or a positive number to find its square root and check the answer.
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Formula and steps included
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Optional learning Learn how this math works See the formula, definitions, and step-by-step method.
Formula
What a square root means
Principal square root: √n = x when x² = n and x ≥ 0
A square root reverses squaring. The √ sign asks for the zero-or-positive number that makes the starting number when multiplied by itself.
A perfect square has a whole-number square root. Other answers may continue forever as decimals, so the calculator shows a rounded value.
How to use the formula
Check the starting number
For an everyday-number answer, the number under the square root must be zero or positive.
Calculate the square root
Use the zero-or-positive answer when you see the √ sign by itself.
Square the answer to check
Multiply the answer by itself. A rounded decimal answer may come back very close to the starting number instead of exactly matching it.
Worked examples
Square root calculator examples
Square root with a decimal answer
√50 can be written exactly as 5 × √2. Its decimal answer is about 7.071067812.
Common questions
Square root calculator FAQ
Why does a positive number have two solutions when squared?
Both x and −x have the same square, but the √ sign asks only for the zero-or-positive answer. That answer is called the principal square root. An equation such as x² = 9 can still have x = 3 and x = −3.
Can I take the square root of a negative number?
Not within the real numbers. Negative radicands require complex numbers, using i where i² = −1.
Why is a square-root answer sometimes rounded?
Some square-root answers are decimals that never end or repeat. The calculator must round those answers to a useful number of digits.
Is the number I enter private?
Your number stays in your browser and is not saved by default or uploaded. Use Save on this device to keep it here, or download a backup file.