## 5. Roots

So far we have looked at powers of ten that are whole number, either greater than one for numbers exceeding ten (eg 100 = 10^{2}), or less than one to represent one divided by the power of ten (eg 1 ÷ 1000 = 0.001 = 10^{-3}). We can also use power notation to represent roots. For instance the square root of one hundred is written as:

√100 = 100^{½} or 100^{0.5}

Using what you learnt about powers of powers in the previous section, you should be able to see that:

100^{0.5} = (10^{2})^{0.5} = 10^{(2 x 0.5)} = 10^{1}

The cube root raises the number to power one-third (e.g. 1000^{0.333}) and the fifth root raises the number to power one-fifth (e.g. 1000^{0.2}).

More generally, the 'xth' root of A is given by A^{(1/x)}.