simplify

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

please explain how to do it I am tierd now

 Rationalize It

1/√2+1 = √2-1

Similarly= 1/√3+√2 = √3-√2

Similarly = 1/√4+√3 = √4-√3

Similarly = 1/√5+√4  = √5-√4

Similarly = 1/√6+√5 = √6-√5

Similarly = 1/√7+√6 = √7-√6

Similarly = 1/√8+√7  = √8-√7

Similarly = 1/√9+√8 = √9-√8

Add

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

-1+3 = 2