Question

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

Answer 1

Multiply the numerator and the denominator by the conjugate of the denominator:

`sqrt(10)/(sqrt(5) - 2)`

`= sqrt(10)/(sqrt(5)-2) * (sqrt(5)+2)/(sqrt(5)+2)`

`= (sqrt(10)*sqrt(5)+2sqrt(10))/(5-4)`

`= 5sqrt(2) + 2sqrt(10)`