surds problem

[fiery123]

Evaluate

1/(1 + 2^0.5) + 1/(2^0.5 + 3^0.5) + ... + 1/(8^0.5 + 9^0.5) + 1/(9^0.5 + 10^0.5)

Dont know how to enter the square root sign so used ^0.5 instead.

[zaza]

These problems are always solved in the same way.

For each individual term:

1/(sqrt(a) + sqrt(b))

multiply by 1, where:

1 = (sqrt(a) - sqrt(b))/(sqrt(a) - sqrt(b))

That gets rid of the sqrts in the denominator and leaves you with integers, thus making it easier to deal with.


zaza

[fiery123]

thanks for that method. It helped a lot. Made it so much easier.
2^0.5 - 1 + 3^0.5 - 2^0.5 + 4^0.5 - 3^0.5 ... = 10^0.5 - 1