Square root calculator
Work out the square root of any non-negative number. The calculator also flags whether the answer is a whole number.
The square root of 144 is 12.0000.
Formula
a is the number under the root. A square root is the number that, squared, gives a.
How we got there
A negative number has no square root among the real numbers — the calculator returns a dash.
How to work out a square root by hand
- Look for a square you know
It pays to know the squares up to 20: 12² = 144, so √144 = 12.
- For other numbers, estimate
√150 lies between 12 and 13, because 12² = 144 and 13² = 169.
- Check by squaring
Square your answer — the original number should come back.
Roots before a test? a lesson with a Mathema tutor
Frequently asked questions
Twelve, because 12 × 12 = 144.
Not among the real numbers. The square of any real number is non-negative.
A root that cannot be written as a fraction — √2 ≈ 1.4142, with a decimal that never terminates.
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