Grade 12 Rationalisation Worksheet
This worksheet focuses on rationalisation of expressions involving surds and algebraic fractions for Grade 12 students.
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Rationalisation Worksheet
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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?
$$1 + \sqrt{2}$$
$$-1 - \sqrt{2}$$
$$\sqrt{2} - 1$$
$$1 - \sqrt{2}$$
7. Rationalise the denominator of the following expression:
$$\frac{x - y}{\sqrt{x} - \sqrt{y}}$$