SOLUTION: Simplest form of ^3squareroot750 + ^3squareroot2058 - ^3squareroot48

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Question 678276: Simplest form of
^3squareroot750 + ^3squareroot2058 - ^3squareroot48

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
To simplify root%283%2C750%29%2Broot%283%2C2058%29-root%283%2C48%29, factor.
Each of those numbers must have a factor that is a perfect cube.
For example, 48=8%2A6=2%5E3%2A6 so

If that expression can be simplified a lot,750 and 2058 must be 6 times the cube of something.

You could methodically do a prime factorization,
and maybe that's what expected,
but maybe you could just find the helpful factors any way that is faster for you.

MY WAY:
750=3%2A250=6%2A125=6%2A5%5E3 and
2058=2%2A1029=2%2A3%2A343=6%2A343=6%2A7%5E3
So