Question

please simplify this question​

Answer 1

Answer:

Hey mate ! above is your answer

Answer 2

Solution :-

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

By rationalising the denominators,

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

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

[ By using identity :-

• ( a + b)^2 = a^2 + b^2 + 2ab

• ( a - b)^2 = a^2 + b^2 - 2ab ]

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

$\frac{8 + 2 \sqrt{15} }{2} + \frac{8 - 2 \sqrt{15} }{2}$

$\frac{8 + 2 \sqrt{15} + 8 - 2 \sqrt{15} }{2}$

$= \frac{16}{2} \\ = 8$

Hence, After simplifing we get 8

Some general points :-

• This Question is solved by the method of rationalisation

• Rationalisation is technique which is generally used to avoid zero in a denominator

• We use rationalisation also to convert the roots into simple numbers in denominators.