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

Algebra ->  Square-cubic-other-roots -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
+root+%283%2C+3%29+%2F+%28sqrt%287%29+%2B+sqrt%2810%29%29+
To rationalize the denominator you must multipy by the conjugate.
or in other words ...
+%28sqrt%287%29+-+sqrt%2810%29%29+
By doing this, when you foil, the middle term will cancel out.
Remember ...
+%28x%2By%29%28x-y%29+=+x%5E2+-+y%5E2+
so ... we will multiply the numerator and denominator by the conjugate.

The denominator then follows the rule and we end up with ...
+%28root+%283%2C+3%29%29%28sqrt%287%29+-+sqrt%2810%29%29+%2F+%287-10%29+
+%28root+%283%2C+3%29%29%28sqrt%287%29+-+sqrt%2810%29%29+%2F+-3+
since the top numbers are cube roots and squareroots ... they can not be combined in radical form.

Answer by dimndskier(8) About Me  (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.