Question

rationalise the denominator of 5+√3÷7-4√3

Answer 1

Ur solution is this

Answer 2

Heya !!!

$\bf \: using \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2}$


$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} }$

On rationalizing the denominator we get,

$= \frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{ 7 + 4 \sqrt{3} } \\ \\ = \frac{5(7 + 4 \sqrt{3}) + \sqrt{3} (7 + 4 \sqrt{3} ) }{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } \\ \\ = \frac{35 + 20 \sqrt{3} + 7 \sqrt{3} + 12 }{49 - 48} \\ \\ = 47 + 27 \sqrt{3}$

Hope this helps ☺