Square Root Calculator

Find the square root of any number, plus the simplified radical form.

What the Square Root Calculator does

The square root of a number is the value that, multiplied by itself, gives that number. Every positive number has two square roots — one positive and one negative — though the radical symbol refers to the positive one.

Formula

  • √x = y where y² = x
  • Simplify by extracting perfect square factors

Inputs explained

InputUnitRequiredNotes
NumbernumberYesAccepts 0 or more.

How to use it

  1. Enter Number.
  2. Select Calculate.

Worked example

Find the square root of 72.

Number
72

√72 ≈ 8.4853, and in radical form 6√2 because 72 = 36 × 2.

Reading the result

  • Every positive number has two square roots, one positive and one negative, though the radical symbol refers to the positive one.
  • A whole-number root means the input is a perfect square, which is what allows a radical to be simplified exactly.

Common mistakes

  • Expecting a real answer from a negative input. Square roots of negatives are imaginary.
  • Confusing the square root with halving. The square root of 16 is 4, not 8.

Frequently asked questions

What is the square root of a negative number?

It is imaginary. √−9 equals 3i, where i is the square root of −1. This calculator works in real numbers only.

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