Question

How do you simplify `root3(216,000)`?

Answer 1

`root(3)(216,000) =60`

Explanation:

Extracting the most obvious cube:
`color(white)("XXX")216,000 = 216 xx 10^3`

Then factor out basic primes until we get to a complete factoring:
`color(white)("XXX")=2xx108xx10^3`

`color(white)("XXX")=2^2xx54xx10^3`

`color(white)("XXX")=2^3xx27xx10^3`

`color(white)("XXX")=2^3xx3xx9xx10^3`

`color(white)("XXX")=2^3xx3^3xx10^3`
`color(white)("XXXXXX")`In practice we probably would have recognized the cube factors before going this far.

Therefore
`color(white)("XXX")root(3)(216,000) = root(3)(2^3xx3^3xx10^3) = 2xx3xx10 =60`