Powers, roots and logarithms

# Surds

A **surd** is a square root which cannot be reduced to a whole number. For example,√4 = 2 is not a surd. But √5 is not a whole number. You could use a calculator to find that but, instead of this, we often leave our answers in the square root form, as a surd. You need to be able to simplify expressions involving surds.

Two surds are equivalent if they express the same number:

You can simplify surds in this way:

Or you can use fraction indices:

**Exercise**: simplify:

solutions: a) 300√2; b) (2/3)

^{5}√2; c) a^{2}b^{3}c^{7}·^{3}√acLicensed under the Creative Commons Attribution Non-commercial Share Alike 3.0 License