Question

How do you simplify `(sqrt 5 + 9 sqrt2)(4 sqrt5 - sqrt 2)`?

Answer 1

`(sqrt5+9sqrt2)(4sqrt5-sqrt2)=2+35sqrt10`

Explanation:

`(sqrt5+9sqrt2)(4sqrt5-sqrt2)`

`=4sqrt5*sqrt5-sqrt5*sqrt2+9sqrt2*4sqrt5-9sqrt2*sqrt2`

`=4(sqrt5)^2-sqrt10+36sqrt10-9(sqrt2)^2`

`=4*5+35sqrt10-9*2`

`=20+35sqrt10-18`

`=2+35sqrt10`