Square Root of Numbers Calculator

When we talk about numbers, a root of a number is another number that produces a whole number when it is raised to a certain power (also called an exponent).

Using the number 64 as an example we can see that the 3rd root of the number is 4:

43 = 4 × 4 × 4 = 64

The third root is also commonly known as the cube root and it is very commonly used for solving cubic equations - in particular, to solve the dimensions of a three dimensional object with a certain volume.

This article is about the more popular and commonly used square root, however.

The square root of a number is the second root. So while 4 is the cube root of 64, it is the 2nd, or square root, of 16:

42 = 4 × 4 = 16

It's likely that you have seen or heard of the square root of a number before and the symbol that accompanies it, which is called the radical symbol: √. Any number that is shown alongside this symbol are called radical terms, or radicals for short.


Enter your number in box A below and click "Calculate" to work out the square root of the given number.


Perfect Square Numbers

When the square root of a given number is a whole number, this is called a perfect square. Perfect squares are important for many mathematical functions and are used in everything from carpentry through to more advanced topics like physics and astronomy.

If we look at the number 16, we know that the square root is 4, and since this is a whole number, we can say that 16 is a perfect square:

√16 = 4

If you want to learn more about perfect square numbers we have a list of perfect squares which covers the first 1,000 perfect square numbers.

Rational and Irrational Numbers

Another common question you might find when working with the roots of a number is whether the given number is rational or irrational. Rational numbers can be written as a fraction and irrational numbers can't.

The quickest way to check if a number is rational or irrational is to determine if it is a perfect square. If it is, then it's a rational number, but if it is not a perfect square then it is an irrational number.

We already know that 16 is a rational number then, because we know it is a perfect square. The number 24, however, is an irrational number because it is not a perfect square:

√24 = 4.899

Practice Square Roots Using Examples

If you want to continue learning about square roots, take a look at the random calculations in the sidebar to the right of this blog post.

We have listed a selection of completely random numbers that you can click through and follow the information on calculating the square root of that number to help you understand number roots.

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