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

1 Answer
May 10, 2018

Answer:

#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#