Question

Rarionalse the denominator of
$\frac{5 + 2 \sqrt{3} }{5 - 2 \sqrt{3} }$
​

Answer 1

Pls mark as brainliest answer

Answer 2

Answer:-

$\sf \frac{5 + \sqrt{3} }{5 - 2 \sqrt{3} }$

$\sf By \: Rationalisation:-$

$\sf \frac{5 + 2 \sqrt{3} }{5 - 2 \sqrt{3} } \times \frac{5 + 2 \sqrt{3} }{5 + 2 \sqrt{3} }$

$\sf \frac{(5 + 2 \sqrt{3})^{2} }{(5 - 2 \sqrt{3})(5 + 2 \sqrt{3}) }$

$\sf \frac{(5)^{2} + (2 \sqrt{3})^{2} + 2 \times 5 \times 2 \sqrt{3} }{(5)^{2} - (2 \sqrt{3})^{2} }$

$\sf \frac{25 + 4 \times 3 + 20 \sqrt{3} }{25 - 4 \times 3 }$

$\sf \frac{25 + 12 + 20 \sqrt{3} }{25 - 12}$

$\sf \frac{37 + 20 \sqrt{3} }{13}$

$\sf \boxed {\frac{37 + 20 \sqrt{3} }{13}}$

$\sf \red {Therefore, \: answer \: is \: \frac{37 + 20 \sqrt{3} }{13}}$