Rationalise the denominator of each of the following:
$\frac{1}{(5 + 3 \sqrt{2})}$

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Solution

On multiplying the numerator and denominator of the given number by $5 - 3 \sqrt{2}$ , we get:
$\frac{1}{5 + 3 \sqrt{2}} = \frac{1}{5 + 3 \sqrt{2}} \times \frac{5 - 3 \sqrt{2}}{5 - 3 \sqrt{2}} = \frac{5 - 3 \sqrt{2}}{{(5)}^{2} - {(3 \sqrt{2})}^{2}} = \frac{5 - 3 \sqrt{2}}{25 - 18} = \frac{5 - 3 \sqrt{2}}{7}$

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