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

1 Answer
Roy Ø.
May 10, 2018

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

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