Question

How do you simplify the cubed root of 150?

Answer 1

`color(green)("Depending on the interpretation of the question:")`

`color(blue)(750sqrt(6)" ") color(brown)(" As an exact value (decimals are not always exact)")`

Explanation:

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.