Square Root Calculator

Calculate the square root of any non-negative number with principal and negative roots and perfect-square detection.

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Result

Square root

4

Positive root

+4

Negative root

-4

Perfect square

Yes

Exact result

Yes

Also in Functions

Algebra

Square root with perfect-square detection

The square root calculator finds the square root of any non-negative number. It shows both the principal (positive) root and the negative root, identifies perfect squares, and flags whether the result is exact or an approximation.

How square roots are calculated

The square root of a number x is the value y such that y × y = x. Every positive number has two square roots: a positive one (the principal root) and a negative one. By convention, the square root symbol refers to the principal root.

Perfect squares — 1, 4, 9, 16, 25, 36, and so on — have integer square roots. Non-perfect squares like 2, 3, and 5 have irrational roots that cannot be expressed as exact fractions.

√x = x^(1/2)

The square root of x is x raised to the power one-half.

Limitations

Square roots of negative numbers are not real. This calculator handles non-negative inputs only.

Frequently asked questions

Is the square root of 2 rational or irrational?

Irrational. It cannot be expressed as a fraction and its decimal expansion (1.41421356...) never terminates or repeats.

Why does every positive number have two square roots?

Because both a positive and a negative number, when squared, give the same positive result. For example, both 3 and -3 squared give 9.

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