Question

Rationalise the denominator

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

Answer 1

Step-by-step explanation:

Given :

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

Solution :

$= > \frac{2}{ \sqrt{5} + \sqrt{3} + 2 } \times \frac{( \sqrt{5} + \sqrt{3} ) - 2}{( \sqrt{5} + \sqrt{3}) - 2 }$

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

$= > \frac{2( \sqrt{5} + \sqrt{3} - 2)}{5 + 3 + 2 \sqrt{5} \sqrt{3} - 4}$

$= > \frac{2( \sqrt{5} + \sqrt{3} - 2)}{4 + 2 \sqrt{15} }$

$= > \frac{ \sqrt{5} + \sqrt{3} - 2 }{2 + \sqrt{15} }$

$= > \frac{ \sqrt{5} + \sqrt{3} - 2 }{2 + \sqrt{15} } \times \frac{2 - \sqrt{15} }{2 - \sqrt{15} }$

$= > \frac{2 \sqrt{5} + 2 \sqrt{3} - 4 - \sqrt{5} \sqrt{15} - \sqrt{3} \sqrt{15} + 2 \sqrt{15} }{ {2}^{2} - ( \sqrt{15} ) ^{2} }$

$= > \frac{2 \sqrt{5} + 2 \sqrt{3} - 4 - 5 \sqrt{3} - 3 \sqrt{5} + 2 \sqrt{15} }{4 - 15}$

$= > \frac{ - \sqrt{5} - 3 \sqrt{3} - 4 + 2 \sqrt{15} }{ - 11}$

$= > \frac{ \sqrt{5} + 3 \sqrt{3} - 2 \sqrt{15} + 4 }{11} .$

Hence :

The rationalise denominator is 11.

Brainly Question Number :

https://brainly.in/question/39934064?utm_source=android&utm_medium=share&utm_campaign=question

Answer 2

Step-by-step explanation:

The rationalise denominator is 11.