Question

How do you simplify `(sqrt10 - sqrt 5) /( sqrt 10 + sqrt 5)`?

Answer 1

`=3-2sqrt2`

Explanation:

`(sqrt10-sqrt5)/(sqrt10+sqrt5)`
Multiplying both the sides by `sqrt(10)-sqrt(5)`
We get
`(sqrt10-sqrt5)^2/((sqrt10+sqrt5)(sqrt10-sqrt5))`
`=(10+5-2timessqrt10timessqrt5)/(10-5)`
`=(15-10sqrt2)/5`
`=5(3-2sqrt2)/5`
`=3-2sqrt2`