Question

10. pls give the ans as soon as possible​

Answer 1

Answer:

Rationalise the denominator first.Then you can simplify it by cancellation and the amswer will be 1

Answer 2

L.H.S =

$\frac{1}{1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} }$

Rationalising each term ,

$(\frac{1}{1 + \sqrt{2} } \times \frac{ 1 - \sqrt{2} }{1 - \sqrt{2} }) + ( \frac{1}{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } ) + ( \frac{1}{ \sqrt{3} + \sqrt{4} } \times \frac{ \sqrt{3} - \sqrt{4} }{ \sqrt{3} - \sqrt{4} } )$

We get,

$\sqrt{2} - 1 + \sqrt{3} - \sqrt{2} + \sqrt{4} - \sqrt{3} \\ = > \sqrt{4} - 1 \\ = > 2 - 1 \\ = > 1$

= R.H.S

Hence , proved .