Question

rationalize the denomination:- 2/(2√11+3√5)​

Answer 1

Step-by-step explanation:

Question:-

rationalize the denominator:-

$\frac{2}{2 \sqrt{11} + 3 \sqrt{5} }$

solution:-

${ \frac{2}{2 \sqrt{11} + 3 \sqrt{5} } \times \frac{2 \sqrt{11} - 3 \sqrt{5} }{2 \sqrt{11} - 3 \sqrt{5} } } \\ \\ \frac{2(2 \sqrt{11} - 3 \sqrt{5}) }{(2 \sqrt{11} ) {}^{2} - (3 \sqrt{5} ) {}^{2} } \\ \frac{4 \sqrt{11} - 6 \sqrt{5} }{4 \times 11 - 9 \times 5} \\ \\ \frac{4 \sqrt{11} - 6 \sqrt{5} }{44 - 45} \\ \\ \frac{4 \sqrt{11} - 6 \sqrt{5} }{ - 1} \\ - (4 \sqrt{11} - 6 \sqrt{5} )$

$\boxed{ \huge \green{answer = - (4 \sqrt{11} - 6 \sqrt{5} )}}$