Question

solve this fast<br />$\frac{1 }{2 + \sqrt{7} } + \frac{1}{ \sqrt{7 } + \sqrt{10} } + ...... + \frac{1}{ \sqrt{28} + \sqrt{31} }$

Answer 1

Replace. 2 with √4
Now,
Divide and multiply in denominator and numerator with congugate of numerator

Refer to attachment ,
On solving we will get,
(√7 - √4 ........√28 - √31)/3
After cancelling out

(√31 - √4)/3

= 1/3{ √31 - √4}