Mathematics

Square Root Calculator

Check a square root and see whether it is exact, approximate, or imaginary.

About this tool

Square Root Calculator calculates results in your browser. Check important financial, medical, or planning decisions with an appropriate professional.

GUIDE

How to use this calculator

Use the square root calculator to identify perfect squares, view exact radical notation for non-perfect squares, and calculate the principal imaginary result for negative numbers.

Calculation method

The square root of x is the value y where y × y = x

Quick examples

√144 = 12
√2 ≈ 1.41421356
√0 = 0
√−9 = 3i

Steps

Enter a positive, zero, or negative number.
Select Calculate square root.
Read the exact form.
Use the decimal approximation when the root is not a whole number.

What is a principal square root?

It is the standard non-negative square root for a non-negative number.

What is a perfect square?

A perfect square has a whole-number square root, such as 144 because 12 × 12 = 144.

Can negative numbers have square roots?

Yes, in the complex-number system. Hypercalcs displays the principal result with i.

Square root calculator

Find the principal square root of positive, zero, or negative numbers.

PRINCIPAL SQUARE ROOT12

This number is a perfect square.

EXACT FORM12

DECIMAL APPROXIMATION12

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