Grade 12 Rationalisation Worksheet

Rationalisation Worksheet

Read each question carefully and rationalize the given expressions. Show all your working.

1. Rationalise the denominator of the following expression:

$$\frac{5}{\sqrt{3}}$$

2. Rationalise the denominator of the following expression:

$$\frac{2\sqrt{x}}{\sqrt{y}}$$

3. Rationalise the denominator of the following expression:

$$\frac{1}{2 + \sqrt{3}}$$

4. Rationalise the denominator of the following expression:

$$\frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} - \sqrt{2}}$$

Complete the steps to rationalise the expression:

5. $$\frac{6}{\sqrt{7} - 2} = \frac{6}{(\sqrt{7} - 2)} \times \frac{(\sqrt{7} + 2)}{(\sqrt{7} + 2)} = \frac{6(\sqrt{7} + 2)}{7 - \text{ }} = \frac{6(\sqrt{7} + 2)}{\text{ }} = \text{ }$$

6. Which of the following is equivalent to $$\frac{1}{1 - \sqrt{2}}$$ after rationalisation?

7. Rationalise the denominator of the following expression:

$$\frac{x - y}{\sqrt{x} - \sqrt{y}}$$