SOLUTION: 8 / cube root of 16

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Question 103966:
8 / cube root of 16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8%2Aroot%283%2C16%29 Start with the given expression

The goal of simplifying expressions with third roots is to factor the radicand into a product of two numbers.
One of these two numbers must be a value in which you can take the third root and still get a rational number.
So let's list the factors of 16
Factors:
1, 2, 4, 8, 16


Notice how 8 is the largest value in which you can take the third root and still get a rational number, so lets break 16 down into 8*2


8%2Aroot%283%2C8%2A2%29 Factor 16 into 8*2

8%2Aroot%283%2C8%29%2Aroot%283%2C2%29 Break up the roots using the identity root%28n%2Cx%2Ay%29=root%28n%2Cx%29%2Aroot%28n%2Cy%29

8%2A2%2Aroot%283%2C2%29 Take the third root of 8 to get 2


16%2Aroot%283%2C2%29 Multiply