How do you simplify #sqrt(4a^6)#?
The square root of
need to divide the given exponent by the value of the root required:
#(2a^3)^2 = 2^2(a^3)^2 = 4a^6#
#(-2a^3)^2 = 4a^6#
What do we mean when we write
So long as the radicand is non-negative, then these symbols refer to the principal non-negative square root.
For any real value of
Note however that
So in order to cover all real values of
#sqrt(4a^6) = abs(2a^3)#
If, in addition we are told that
#sqrt(4a^6) = 2a^3#