Square Root Calculator

The square root of x is the number that multiplied by itself gives x. Any root is a fractional power: the kth root of x is x raised to the power of 1/k. Simplifying a radical means pulling out the largest perfect square factor: sqrt(72) = sqrt(36 x 2) = 6 sqrt(2).

What is the square root of 72?

About 8.485. In exact form it is 6 times the square root of 2, because 72 is 36 times 2 and 36 is a perfect square.

Can you take the square root of a negative number?

Not within the real numbers. Mathematicians handle it with imaginary numbers, writing the square root of -9 as 3i. Odd roots are fine though: the cube root of -8 is -2.

What is a perfect square?

A number whose square root is a whole number: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 and so on. Every other number has a root that runs on forever without repeating.

Does a number have two square roots?

Yes. Both 5 and -5 square to 25. By convention the square root symbol means the positive one, which is what this page shows, but when solving an equation you have to allow for both.