##color(green)(“Depending on the interpretation of the question:”)##
##color(blue)(750sqrt(6)” “) color(brown)(” As an exact value (decimals are not always exact)”)##
Braking the question down into its component parts:
Cube##color(red)(“d”) -> (?)^3## root of 150##->(sqrt(150))^3##
If the question had read: “cube root of 150 ” we would have ##root(3)(150)##
Although, it is not common for people just say “root” for “square root”. However, I have come across it being used in that way.
Thus there could be a contradiction in meaning of the question! ‘~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)(“Solution for ‘cubed root'”)##
Consider the prime factor tree of 150
We observe that 150 can be broken down to ##2xx3xx5^2##
So ##sqrt(150)=sqrt(2xx3xx5^2) = 5sqrt(6)## giving
##(sqrt(150))^3 = (5sqrt(6))^3##
This gives us
##5sqrt(6)xx5sqrt(6)xx5sqrt(6)##
##5^3xx(sqrt(6))^2xxsqrt(6)##
##125xx6xxsqrt(6)##
##color(blue)(750sqrt(6)” “)color(brown)(” As an exact value (decimals are not always exact”)## ‘~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
##color(blue)(“Solution for ‘cube root'”)##
##root(3)(150)##
George is correct. This can not be simplified any further.
