Question

Rationalise the denominator

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

Answer 1

Hola Mate!!

Your answer :-

$= > \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \\ \\ = > \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} } \\ \\ = > \frac{ {(5 + \sqrt{3} )}^{2} }{ {( 5 )}^{2} - { (\sqrt{3} )}^{2} } \\ \\ = > \frac{ ({5})^{2} + {( \sqrt{3} )}^{2} + 2 \times 5 \times \sqrt{3} }{25 - 3} \\ \\ = > \frac{25 + 3 + 10 \sqrt{3} }{22} \\ \\ = > \frac{28 + 10 \sqrt{3} }{22} \\ \\ = > \frac{14 + 5 \sqrt{3} }{11}$

☆ Hope it helps ☆

Answer 2

$\frac{5 + \sqrt{3} }{5 - \sqrt{3} } \\ = \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \times \frac{ \sqrt{3 } + 5}{ \sqrt{3} + 5} \\ = \frac{5 \sqrt{3} + 25 + 3 + 5 \sqrt{3} }{ {5}^{2} - { (\sqrt{3} )}^{2} } \\ = \frac{10 \sqrt{3} + 28 }{25 - 3} \\ = \frac{ 10\sqrt{3} + 28 }{22} \\ = \frac{2(5 \sqrt{3} + 14)}{22} \\ = \frac{5 \sqrt{3} + 14}{11}$
Heyy friend your answer is here