Description

Sometimes you just can’t beat some repetitive question completion. This rationalising the denominator worksheets pack contains 1560 questions and answers spread across 30 separate PDF documents.

Having multiple worksheets is incredibly useful if you wish to give each student a different set of questions.

How do you rationalise the denominator?

Let’s take an example question:

$$
\begin{aligned}
& \frac{2}{3-\sqrt{5}} \\\\
= & \space \frac{2}{3-\sqrt{5}} \times \frac{3+\sqrt{5}}{3+\sqrt{5}} \\\\
= & \space\frac{2(3+\sqrt{5})}{9-5} \\\\
= & \space\frac{2(3+\sqrt{5})}{4} \\\\
= & \space\frac{3+\sqrt{5}}{2}
\end{aligned}
$$

The trick is to multiply the original expression by the conjugate of the denominator. You are not changing the value of the expression since you are only multiplying by 1.  This eliminates the root from the denominator.