Question

How do you simplify the square root of -8/9?

Answer 1

`sqrt(-8/9)=2/3sqrt(2)i`

Explanation:

You want to know `sqrt(-8/9)`

We note that `8=2^3` and `9=3^2`, and also `sqrt(-1)=i`

Therefore
`sqrt(-8/9)=sqrt(-1*2^3/3^2)`
`=sqrt(2^3)/sqrt(3^2)sqrt(-1)`
`=2/3sqrt(2)i`