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Rationalisation

Rationalise t...

Question

Rationalise the denominator of $\frac{1}{7 + 4 \sqrt{3}}$

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Solution

$\frac{1}{7 + 4 \sqrt{3}}$
$(7 - 4 \sqrt{3})$
$\frac{1 \times (7 - 4 \sqrt{3})}{(7 + 4 \sqrt{3}) (7 - 4 \sqrt{3})}$
$= \frac{7 - 4 \sqrt{3}}{(7)^{2} - (4 \sqrt{3})^{2}}$
$= \frac{7 - 4 \sqrt{3}}{49 - 48}$
$= 7 - 4 \sqrt{3}$

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