Question

Simplify 1/1+root2 + 1/root2+root3 +2/root3+root5

Answer 1

Answer:

1 /1+root 2 + 1/root2+root3 +1/root3 +root4 + ...................+ 1/root8+root9

1/(1 + √2) + 1/(√2 + √3) + 1/(√3 + √4) + 1/(√4 + √5) + 1/(√5 + √6) + 1/(√6 + √7) + 1/(√7 + √8) + 1/(√8 + √9)

Rationalizing each term

1/(1 + √2) = ((√2- 1))/((√2+ 1) (√2- 1) ) = ((√2- 1))/((〖√2〗^2- 1)) = √2-1

We will get similar result like above for all the terms

= √2 – 1 + √3 - √2 + √4 - √3+ √5 - √4 + √6 - √5 + √7 - √6 + √8 - √7 + √9 - √8

=√9 – 1

=3 – 1

= 2