## Exponents and Square Roots

If a number is multipled together several times e.g. 3 × 3 × 3 × 3 × 3 if can be written in exponent form, 34

In the number 34, the 3 is called the base and the 4 is called the exponent, index orpower.

All mean the same thing!

Examples

 32 9 33 27 34 81

### Prime Factors

Natural numbers can be written as the product of prime numbers. These are best written in index form.

e.g. 36 = 2 × 2 × 3 × 3 = 22 × 32
12 = 2 × 2 × 3 = 22 × 3

Factor trees are useful for finding prime factors. ### Square Roots

Squaring a number means multiplying it by itself.e.g. 32 = 3 × 3 = 9

Finding the square root of a number is the opposite or inverse of doing this.e.g. i.e. A number must be found which multiplies with itself to give the original number,

Some common square roots

 1 4 9 16 25 36 49 64 81 100 121 144 400 10 000 1 000 000 1 2 3 4 5 6 7 8 9 10 11 12 20 100 1000

To find the square roots of numbers between the ones shown above, the easiest way is to use a calculator.

e.g. (rounded to 3 decimal places).