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

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##