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:

- 7
- 11
- 15

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

1.

=

=

=

=

2. Multiply

First multiply the whole numbers:

Then multiply the surds:

This makes:

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:

So the answer is:

- Question
- Simplify
- Simplify
- Multiply out

- 6