Calculate the value of the sum 1/(sqrt1+sqrt2) + 1/(sqrt2+sqrt3) + 1/(sqrt3+sqrt4) + ...+1/(sqrt99+sqrt100)

1/(sqrt1+ sqrt2)
+ 1/(sqrt2 + sqrt3) + ....+ 1/(sqrt99+ sqrt100)

We know that:

1/(sqrta + sqrt(1+a) = sqrt(a+1) -sqrta

==>sqrt2 - sqrt1 + sqrt3
-sqrt2 + ...+ sqrt100 -sqrt99

= -sqrt1 + sqrt100

= -1 +
10

= 9