How do you simplify #sqrt(9e^6)#?
1 Answer
Answer:
It depends what you mean by
Explanation:

If
#e# is the mathematical constant (#~~2.7182818# ), then the answer is definitely#3e^3# . 
If
#e# is a Real valued variable, then#3abs(e^3)# covers both positive and negative values of#e# . 
If
#e# is a Complex valued variable then#3sqrt(e^6)# is about the best you can do.
The square root symbol
We have:
#(3e^3)^2 = 3^2(e^3)^2 = 9e^6#
#(3e^3)^2 = (3)^2(e^3)^2 = 9e^6#
So regardless of the value of
If
If
So if
How about the Complex case?
Suppose
Then:
#3e^3 = 3(cos((3pi)/4)+i sin((3pi)/4))#
#sqrt(9e^6) = 3sqrt(cos((6pi)/4)+i sin((6pi)/4))#
#=3sqrt(cos(pi/2)+i sin(pi/2))#
#=3(cos(pi/4)+i sin(pi/4))#
#=3(cos((3pi)/4)+sin((3pi)/4))#
#=3e^3#
So in the general Complex case, about the best we can say is:
#sqrt(9e^6) = +3e^3#
or better:
#sqrt(9e^6) = 3sqrt(e^6)#
It would be possible to pick out individual cases according to their