When a fraction has a denominator which is rational, the fraction is simplified by rationalising its denominator. To rationalise the denominator of a fraction, both its numerator and denominator are multiplied by the conjugate surd of the denominator.
\( \frac{3}{5 + \sqrt{2}} \times \frac{5 - \sqrt{2}}{5 - \sqrt{2}} \)

When a fraction has a denominator which is rational, the fraction is simplified by rationalising its denominator.
To rationalise the denominator of a fraction, both its numerator and denominator are multiplied by the conjugate surd of the denominator.

\( \frac{3}{5 + \sqrt{2}} \times \frac{5 - \sqrt{2}}{5 - \sqrt{2}} \)

Rationalising the Denominator

Rationalising the Denominator