How do I 'simplify' a surd?

Simplifying a surd means to express it using smaller numbers, making it easier to use in calculations. There are a couple of facts you will need to learn about surds, these are, 1) sqrt(a x b) = sqrt(a) x sqrt(b), and 2) sqrt(a/b) = sqrt(a)/sqrt(b), these will be useful tools for solving problems.
Now let's use the example 'Simplify sqrt(48)'. Using fact 1) above we will split 48 into 2 factors, specifically looking for a square factor - we have 4 x 12 and 16 x 3, as 16 is the biggest we will use 48 = 16 x 3. So, sqrt(48) = sqrt(16 x 3) = sqrt(16) x sqrt(3) = 4 x sqrt(3), or more neatly 4sqrt(3). Let's do another...