Square Root Calculator

What This Square Root Calculator Does

Find the square root of a number as a decimal. For whole numbers it also shows the simplified radical form (for example, √50 = 5√2).

How It Works

square root: √n is the number that, multiplied by itself, gives n
simplified radical: pull out the largest perfect-square factor

For 50: the largest perfect-square factor is 25, and √25 = 5, so √50 = 5√2.

How to Use It

1. Enter a number (zero or more).
2. Read the decimal square root and, for whole numbers, the simplified radical.

Worked Examples

Number	Square root	Simplified
49	7	perfect square
50	7.0711	5√2
2	1.4142	√2
72	8.4853	6√2
100	10	perfect square

FAQ

How do you find a square root by hand?

For perfect squares, recall the factor that squares to the number (7 x 7 = 49, so √49 = 7). Otherwise estimate between known squares, or use this calculator for the decimal value.

What is a simplified radical?

It pulls the largest perfect-square factor out of the root. √72 = √(36 x 2) = 6√2.

Can you take the square root of a negative number?

Not within the real numbers — a negative number has no real square root. This tool reports that.

Is the decimal exact?

Square roots of non-perfect-squares are irrational (never-ending), so the decimal is rounded here to a few places; the simplified radical is the exact form.