# Surd simplification

1. Jan 31, 2005

### Gughanath

p = root 2 q = root 3
(root 18 + root 12) / (root 8 - root 96) , write this in terms of p and q in its simplest form. I keep getting the wrong answer, please help!

2. Jan 31, 2005

### Nylex

Post your working, so people can show you where you've gone wrong.

3. Jan 31, 2005

### dextercioby

Do you know how to decompose natural numbers into prime factors...??

Daniel.

4. Jan 31, 2005

### Gughanath

yes, but i dont end up with the answer i was meant to!

5. Jan 31, 2005

### dextercioby

Why not???
$$\sqrt{18}=3\sqrt{2}=3p$$

Can u handle the other ones...?

Daniel.

6. Jan 31, 2005

### The Bob

$$p = \sqrt{2}$$ , $$q = \sqrt{3}$$

$$\frac{(\sqrt{18} + \sqrt{12})}{(\sqrt{8} - \sqrt{96})}$$

Personally I just try to make the numbers with the smallest number of terms possible.

E.g. $$\sqrt{18} = \sqrt{3 \times 3 \times 2} = pqq$$ or $$p2q$$ or $$\sqrt{18} = 3 \sqrt{2} = 3p$$