SOLUTION: Simplify {{{root(3,40a^3b^6c^8)}}}

Question 148124: Simplify
Found 2 solutions by jim_thompson5910, vleith:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Factor into . Notice how 8 is a perfect cube (ie ).

Factor into . Once again, notice how is a perfect cube.

Factor into . Once again, notice how is a perfect cube.

I'm breaking the expression into perfect cubes so that when I take the cube root of these cubes, I'll be left with the expression itself. Since is a perfect cube, this means that . Also, since is a perfect cube, this means that .

Break up the root.

Take the cube root of the perfect cubes to get just the base of the expression.

Recombine any roots leftover and multiply

So simplifies to

In other words, .

Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!

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