Question

How do you simplify `0.5sqrt200 - sqrt(-32)`?

Answer 1

`(5sqrt(8))/2-4sqrt(-2)` or `(5sqrt(8))/2-4isqrt(2)`

Explanation:

`200` can be rewritten as `25x8`, so `sqrt(200)=sqrt(25x8)=sqrt(25)sqrt(8)=5sqrt(8)`

`5sqrt(8)*1/2=(5sqrt(8))/2`

`sqrt(-32)` is impossible to write as a real number so it is taken as `(5sqrt(8))/2-sqrt(-32)`, however `sqrt(x), x<0, = sqrt(abs(x))*i`.

`-32 = -2*16 or 2*-16`. Therefore `sqrt(-32)` is equal to:
`sqrt(-2*16)=sqrt(-2)sqrt(16)=4sqrt(-2)=4*sqrt(2)i=4isqrt(2)`, or
`sqrt(2*-16)=sqrt(2)sqrt(-16)=sqrt(2)4i=4isqrt(2)`

So it can be written as `(5sqrt(8))/2-4isqrt(2)`