Question

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} }$
Rationalise the denominator.

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get\\ \\ = \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{5 \times 7 - 5 \times 4 \sqrt{3} + 2 \sqrt{3} \times 7 - 2 \sqrt{3} \times 4 \sqrt{3} }{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } \\ \\ = \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{49 - 48} \\ \\ = 11 - 6 \sqrt{3}$

Hope this helps!!!

@Mahak24

Thanks....
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