Question

How do you simplify `sqrt(-4/5)`?

Answer 1

`sqrt(-4/5) = i sqrt(4/5) = (2sqrt(5))/5 i`

Explanation:

By definition and convention, if `x < 0` then `sqrt(x) = i sqrt(-x)` where `i` is the imaginary unit.

Also, if `a, b > 0` then `sqrt(ab) = sqrt(a)sqrt(b)`

So:

`sqrt(-4/5) = i sqrt(4/5) = i sqrt(4/25 * 5) = i sqrt(4/25)sqrt(5) = i sqrt((2/5)^2)sqrt(5)`

`= (2sqrt(5))/5 i`