Question

How do you rationalize the denominator and simplify `sqrt35 /sqrt55`?

Answer 1

You can rationalize a radical denominator by multiplying the radical by itself.

e.g. `sqrt8` x `sqrt8` = 8
`sqrt3` x `sqrt3` = 3
`sqrt5`x`sqrt5`=5

However, by multiplying the radical denominator by a number, you have to do the same for the numerator.

`sqrt35/sqrt55` x `sqrt55/sqrt55`= (`sqrt7`x`sqrt5`x`sqrt5`x`sqrt11)` `/55` = `(5sqrt77)/55`=`(sqrt77)/11`