# Multiplying and dividing surds

### Multiplying surds with the same number inside the square root

We know that:

So multiplying surds that have the same number inside the square root gives a whole, rational number.

Question

Simplify the following surds:

1. 7
2. 11
3. 15

## Multiplying surds with different numbers inside the square root

First, simplify the numbers inside the square roots if possible, then multiply them.

### Examples

1.

=

=

=

=

2. Multiply

First multiply the whole numbers:

Then multiply the surds:

This makes:

## Dividing surds

Just like the method used to multiply, the quicker way of dividing is by dividing the component parts:

Divide the whole numbers:

Divide the square roots: