SOLUTION: what is the cubed root of -432

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Question 259334: what is the cubed root of -432
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
-432 is not a perfect cube. So it is impossible to find the cube root of -432 exactly.

But -432 does have perfect cube factors so we can simplify it. 8 is 2 cubed and 8 happens to divide evenly into 432. To get the minus sign out of the way, I am going to factor out -8:
root%283%2C+-432%29+=+root%283%2C+-8%2A54%29
Using the property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29, we can separate out the perfect square factor:

When you reduce fractions you keep reducing until the fraction cannot be reduced any further. Simplifying radicals is similar. Keep simplifying until you cannot simplify any further. So we look at the remaining radical and look for more perfect cube factors. 8 is not a factor of 54. But 27, which is 3 cubed, is a factor of 54:

Using the property of radicals to separate the perfect cube factor again we get:

This cannot be simplified any further.

So a simplified expression for the cube root of -432 is -6root%283%2C2+%29