# SQUARE AND SQUARE ROOT

##### HELLO, WELCOME BACK TO CLASS

Square of Numbers

The square of a number is the number multiplied by itself.

## How to Square A Number

To square a number: multiply it by itself.

3 squared =32 = 3×3 = 9

Squared” is often written as a little 2 like this:
This says “4 Squared equals 16”
(the little 2 says the number appears twice in multiplying)

## Squares From 02 to 62

 0 Squared = 02 = 0 × 0 = 0 1 Squared = 12 = 1 × 1 = 1 2 Squared = 22 = 2 × 2 = 4 3 Squared = 32 = 3 × 3 = 9 4 Squared = 42 = 4 × 4 = 16 5 Squared = 52 = 5 × 5 = 25 6 Squared = 62 = 6 × 6 = 36

Square Root

Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that number times itself.

The square root of a number, n, written below is the number that gives n when multiplied by itself.

Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson, has an inverse too, called “finding the square root.” Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …

The square root of a number, n, written

is the number that gives n when multiplied by itself. For example,

because 10 x 10 = 100

Examples

Here are the square roots of all the perfect squares from 1 to 100.

## 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!

We use it like this:

and we say “square root of 9 equals 3”

### Example: What is √25?

25 = 5 × 5, in other words when we multiply 5 by itself (5 × 5) we get 25

√25 = 5

But wait a minute! Can’t the square root also be −5? Because (−5) × (−5) = 25 too.

• Well the square root of 25 could be −5 or +5.
• But when we use the radical symbol √ we only give the positive (or zero) result.

### Example: What is √36 ?

Answer: 6 × 6 = 36, so √36 = 6

Try to remember them up to 12.

## Perfect Squares

The Perfect Squares (also called “Square Numbers”) are the squares of the whole numbers:

 Perfect Squares 0 0 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144 13 169 14 196 15 225 etc…

Quiz

1. What is the square root of 8?
2. What is the square root of 9?
3. What is the square root of 10?
4. What is 1 squared?
5. What is 1.1 squared?

What is 2.6 squared?

Your Opinion Matters! Quickly tell us how to improve your Learning Experience HERE