Square roots

The opposite of squaring a number is called finding the square root.

See some examples here.

A square root of a number is a value that can be multiplied by itself to give the original number.

A square root of 9 is 3, because when 3 is multiplied by itself you get 9.

It is like asking:

What can I multiply by itself to get this?

To help you remember think of the root of a tree: "I know the tree, but what is the root that produced it?" In this case the tree is "9", and the root is "3"

Here are some more squares and square roots:

4		16
5		25
6		36

These are the first perfect squares:

It is easy to work out the square root of a perfect square, but it is really hard to work out other square roots.

Example: what is √10?

Well, 3 × 3 = 9 and 4 × 4 = 16, so we can guess the answer is between 3 and 4.

• Let's try 3.5: 3.5 × 3.5 = 12.25
• Let's try 3.2: 3.2 × 3.2 = 10.24
• Let's try 3.1: 3.1 × 3.1 = 9.61
• ...

Getting closer to 10, but it will take a long time to get a good answer!

At this point, I get out my calculator and it says: 3.1622776601683793319988935444327 But the digits just go on and on, without any pattern. So even the calculator's answer is only an approximation !

The Easiest Way to Calculate a Square Root

Use your calculator's square root button!

(And also use your common sense to make sure you have the right answer)