Question 346817: the cubic square root of 9000?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website!  is called "the cube root of 9000".
Just like you should try to reduce fractions, you should try to simplify square, cube, 4th, etc. roots. To simplify a cube root, you try to find perfect cubes which are factors of the radicand (the expression inside the radical).
So to simplify we look for perfect cube factors of 9000, if any. After a little thought we might realize that 1000 is  and it is clearly a factor of 9000. So we can rewrite our cube root:
Now we can use a property of radicals,  , to separate the perfect cube factor(s) into their own cube roots:
Now we can replace the cube root of the perfect cube:
This is the simplified, exact expression for the cube root of 9000.
If you need a decimal approximation for a cube root, just take advantage of the fact that a cube root can be expressed as a fractional exponent. Then you can use your calculator to find a cube root by raising the radicand to the 1/3 power. If your calculator supports parentheses, "(" and ")", then you can type:
10*3^(1/3)
If your calculator does not support use of parentheses, you could type:
10*3^0.333333
(since 0.33333 is a decimal approximation for 1/3).
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