SOLUTION: Hello. The problem is cube root of 3 / square root of 7 + square root of 10. The directions say rationalize the denominator and assume that all variables represent positive real nu

Question 33984: Hello. The problem is cube root of 3 / square root of 7 + square root of 10. The directions say rationalize the denominator and assume that all variables represent positive real numbers. I have come up with the square root of 3. Can someone please verify if I have the correct answer? Thanks in advance.
Found 2 solutions by Cintchr, dimndskier:
Answer by Cintchr(481) (Show Source): You can put this solution on YOUR website!

To rationalize the denominator you must multipy by the conjugate.
or in other words ...

By doing this, when you foil, the middle term will cancel out.
Remember ...

so ... we will multiply the numerator and denominator by the conjugate.

The denominator then follows the rule and we end up with ...

since the top numbers are cube roots and squareroots ... they can not be combined in radical form.

Answer by dimndskier(8) (Show Source): You can put this solution on YOUR website!
You have provided no variables in this problem.
However, it does not seem that there is a rational answer either, since the cube root of three IS repeating, and so are the square roots of 7 and 10 both.
However, this is what I came up with -1*{((3)^(1/3))}/3.
This is the first problem I have solved on this website, so I need to go back and learn the syntax better, but write that out on paper and remain aware of the parenthesis and braces.
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