Square Root Calculator

What a Square Root Means

A square root undoes squaring. Since $7 \times 7 = 49$, the square root of 49 is 7.

The name comes from area. $\sqrt{n}$ is the side length of a square whose area is $n$ - which is exactly what the figure shows: a square with area 50 has sides of length $\sqrt{50} \approx 7.07$. So “what is $\sqrt{50}$?” is really the question “how long is each side of a square that covers 50 squares of space?”

A few numbers come out even - 49, 100, and 144 are perfect squares. Most do not, and their square root is a never-ending decimal. Even then it can be written exactly as a simplified radical by pulling out the largest perfect-square factor: for 50, that factor is 25, and since $\sqrt{25} = 5$, we get $\sqrt{50} = 5\sqrt{2}$.

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. $\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}$.

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.