Square: Square of whole numbers

To square a number, just multiply it by itself 

"Squared" is often written as a little 2 like this:

Squares From 1² to 6²

You can also find the squares on the Multiplication Table:

Negative Numbers

You can also square negative numbers.

What happens when you square (-5) ?

(-5) × (-5) = 25

(a negative times a negative gives a positive)

When you square a negative number you get a positive result.

Just the same as if you had squared a positive number:

Square Roots

A square root goes the other way

4 squared is 16, so a square root of 16 is 4 

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

Example

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

The Square Root Symbol

This is the special symbol that means "square root", it is sort of like a tick,
and actually started hundreds of years ago as a dot with a flick upwards.

It is called the radical, and always makes mathematics look important!

 You can use it like this:

you would say "square root of 9 equals 3"

Example:

What is √25?

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

Note: Numbers like that are called Irrational Numbers.

A Fun Way to Calculate a Square Root

There is a fun method for calculating a square root that gets more and more accurate each time around:

1. Start with a guess (let's guess 4 is the square root of 10)
2. divide by the guess (10/4 = 2.5)
3. add that to the guess (4 + 2.5 = 6.5)
4. then divide that result by 2, in other words halve it. (6.5/2 = 3.25)
5. now, set that as the new guess, and start at 2.again

• Our first attempt got us from 4 to 3.25
• Going again (2 to 5) gets us: 3.163
• Going again (2 to 5) gets us: 3.1623

And so, after 3 times around the answer is 3.1623, which is pretty good, because:

3.1623 x 3.1623 = 10.00014

Now ... why don't you try calculating the square root of 2 this way?

How to guess

What if you have to guess the square root for a difficult number such as "82,163" ... ?

In that case I would think to myself "82,163" has 5 digits, so the square root might have 3 digits (100x100=10,000), and the square root of 8 (the first digit) is about 3 (3x3=9), so 300 would be a good start.

Play this video to learn more about square roots