Simplify 1/(sqrt(45) + sqrt(36)) + 1/(sqrt(36) + sqrt(27)) + 1/(sqrt(27) + sqrt(18)) + 1/(sqrt(18) + sqrt(9))
+241 Ill give you some hints:
sqrt(45) = sqrt(9*5) = 3 sqrt(5)
sqrt(36) = 6
sqrt(27) = sqrt(3*3*3) = 3 sqrt(3)
sqrt(18) = sqrt(9*2) = 3 sqrt(2)
sqrt(9) = 3
It should be easy from here, just plug in the simplified version in for the unsimplifiied, and then you will see what to do from there! 
