Question

How do you divide `sqrt7/(sqrt34+5)`?

Answer 1

This can be simplified a bit by removing the radical from the denominator.
To do this recall that
`(a + b) * (a - b) = (a^2 - b^2)`
or, for our particular case
`(sqrt(34) + 5) * (sqrt(34) - 5) = 34 -25 = 9`

Applying this to the original problem:
`sqrt(7)/(sqrt(34)+5)`

`= sqrt(7)/(sqrt(34)+5) * (sqrt(34)-5)/(sqrt(34)-5)`

`= ((sqrt(7)) (sqrt(34) - 5))/9`

(The numerator could be multiplied but doing so provides not obvious simplification.)