Watch this video to learn about the rules of surds.
A surd is a square root which cannot be reduced to a rational numberA number that can be written in fraction form. This includes integers, terminating decimals, repeating decimals and fractions..
For example, \(\sqrt 4 = 2\) is not a surd.
However \(\sqrt 5\) is a surd.
If you use a calculator, you will see that \(\sqrt 5 = 2.236067977...\) and we will need to round the answer correct to a few decimal places. This makes it less accurate.
If it is left as \(\sqrt 5\), then the answer has not been rounded, which keeps it exact.
Here are some general rules when simplifying expressions involving surds.
\(\sqrt a \times \sqrt a = a\)
\(\sqrt {ab} = \sqrt a \times \sqrt b\)
\(\sqrt {\frac{a}{b}} = \frac{{\sqrt a }}{{\sqrt b }}\)
Now use the information above to try the example questions below.