Enter a number to get its square root as a decimal and, where possible, the simplified radical form. The factoring steps are shown below the result.
Try a perfect square like 144, or a number with a square factor like 72.
The square root of a number n is the value that, multiplied by itself, equals n. The radical symbol is the check-mark sign placed over the number.
When n is a perfect square the root is a whole number: sqrt(144) = 12 because 12 x 12 = 144. When n is not a perfect square, the root is irrational, so the calculator returns a decimal rounded to several places and, when a perfect-square factor exists, the simplified radical form.
72 is not a perfect square, but it has a perfect-square factor. Break it down step by step.
For background on radicals and irrational roots, see Wolfram MathWorld on the square root.
Find a number that multiplies by itself to give your value. For perfect squares like 144 the answer is exact (12). For others, estimate between the two nearest perfect squares, then refine.
It pulls the largest perfect-square factor out of the radical. For example sqrt(72) = sqrt(36 x 2) = 6 sqrt(2).
Not within the real numbers. The square root of a negative number is imaginary, written with i, such as sqrt(-9) = 3i.
Yes. This tool accepts decimals and returns the decimal root rounded to several places.
Editor at Encore Editorial, Chris Terry sets the editorial standards here and turns dense topics into plain English. He has written widely on education, finance, and consumer markets.