How do I simplify surds?

In order to simplify a surd you need to look at the factors of the number under the square root. You can then multiply together the square roots of the factors.

For example if you wanted to simplify sqrt(12), its factors are 1 and 12, 2 and 6, 3 and 4. You need to look for the pair of factors with a square number. In this example, we choose 3 and 4 because 4 is a square number. We know sqrt(3x4) = sqrt(3) x sqrt(4) = sqrt(12). Because sqrt(4) = 2 the simplified surd is 2sqrt(3).