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Square Root calculator
Square Root calculator
Enter your values below and press Calculate to see your result instantly.
√
Radicand (Area)
The Principal (Positive) Root
16.0000
SECONDARY ROOT
-16.0000
PERFECT SQUARE?
Yes
Area
Geometrically, a 2D square with an area of 256 requires side lengths measuring exactly 16.
About the Square Root calculator
Find the square root of any positive number, including numbers that are not perfect squares.
How to use the Square Root calculator
- Enter the number.
- Press Calculate to see the square root.
Formula and method
The square root of x is the number y such that y × y = x.
Worked example
√144 = 12. √2 ≈ 1.41421, an irrational number that never ends or repeats.
A non-perfect square. √50 ≈ 7.0711. Because 7² = 49 and 8² = 64, the root of 50 lies just above 7.
When to use the Square Root calculator
- Finding side lengths from areas.
- Working out the hypotenuse in the Pythagorean theorem.
- Estimating a root without a table.
Common mistakes to avoid
- Taking the square root of a negative number and expecting a real result.
- Forgetting that a positive number has two square roots, positive and negative.
Tips
- Perfect squares (1, 4, 9, 16, 25...) have whole-number roots.
- The square root of a negative number is not a real number.
Frequently Asked Questions
Find the two perfect squares either side of the number. √50 is between √49 = 7 and √64 = 8, so about 7.07.
A number whose square root is a whole number, such as 16, 25 and 36.
A root that cannot be written as a fraction, such as √2. Its decimals go on forever without repeating.