Roots, for example $\sqrt{2}$, $\sqrt{3}$, $\sqrt[3]{6}$ are also known as surds.
A common cause of error is misuse of expressions involving surds.
You should be aware that $\sqrt{ab}=\sqrt{a} \sqrt{b}$ but $\sqrt{a + b}$ is NOT equal to $\sqrt{a} + \sqrt{b}$.
Rationalise the Denominator
Write the following with no surd in the denominator.
Simplification
Single Root
Mixed Fractions
A mixed fraction has a whole number part and a fractional part. For example, $13/5$ can be written as the mixed fraction $2+ \frac{3}{5}$. Remember to put a + between the integer and the fraction.
Improper Fractions
An improper fraction is 'top-heavy'. Its numerator is greater than its denominator. For example, the mixed fraction $13 \frac{4}{5}$ can be written as the improper fraction $69/5$.
