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Surds - AQARationalising denominators - Higher

Surds are numbers left in square root form that are used when detailed accuracy is required in a calculation. They are numbers which, when written in decimal form, would go on forever.

Part of MathsNumber

Rationalising denominators - Higher

A fraction with a surd in the denominator can be simplified so that the denominator is an integer. This is called the denominator.

Example

Simplify \(\frac{\sqrt{8}}{\sqrt{6}}\)

First simplify \(\sqrt{8}\).

\(\sqrt{8} = \sqrt{4 \times 2}\)

\(= \sqrt{4} \times \sqrt{2}\)

\(= 2\sqrt{2}\)

Then multiply the numerator and denominator by \(\sqrt{6}\).

\(\frac{2\sqrt{2} \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}}\)

\(= \frac{2\sqrt{12}}{6}\)

\(= \frac{4\sqrt{3}}{6} = \frac{2\sqrt{3}}{3}\)

Question

Rationalise the denominator of the following:

  1. \(\frac{1}{\sqrt{2}}\)
  2. \(\frac{\sqrt{3}}{\sqrt{2}}\)
  3. \(\frac{5}{2 \sqrt{3}}\)