Question

How do you simplify `(2 sqrt5 )/ (sqrt2 +5)`?

Answer 1

(2sqrt(10)-10sqrt(5))/27)

Explanation:

Use the conjuguate first :
`(2sqrt(5))/(sqrt(2)+5)=(2sqrt(5)(sqrt(2)-5)) /((sqrt(2)+5)(sqrt(2)-5))`
Also `(a+b) (a-b) =a²-b²`, so finally :
`(2sqrt(5))/(sqrt(2)+5)=(2sqrt(10)-10sqrt(5)) /27`