Question

Rationalise the denominator of 5/2+ root 3

Answer 1

$\frac{5}{2 + \sqrt{3} } \\ = \frac{5}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ = \frac{5(2 - \sqrt{3} )}{(2 + \sqrt{3})(2 - \sqrt{3}) } \\ the \: denominator \: is \: in \: the \: form \: (a + b)(a - b) = {a}^{2} - {b}^{2} \\ = \frac{10 - 5 \sqrt{3} }{ {2}^{2} - ( \sqrt{3} ) ^{2} } \\ = \frac{10 - 5 \sqrt{3} }{4 - 3} \\ = \frac{10 - 5 \sqrt{3} }{1}$