Question

How do you rationalize the denominator and simplify `sqrt(10)/(sqrt(5)-2)`?

Answer 1

You first multiply top and bottom with `sqrt5+2`

This will give the special product `A^2-B^2` as denominator

`=sqrt10/(sqrt5-2)*(sqrt5+2)/(sqrt5+2)`

`=(sqrt(2*5)*sqrt5+2sqrt10)/(sqrt5^2-2^2)`

`=(sqrt(2*5^2)+2sqrt10)/(5-4)`

`=5sqrt2+2sqrt10`