SOLUTION: Question- How can you write the expression with rationalized denominator? 2 plus square root of 3 (with index root of 3) over square root of 6 also with index root of 3

Algebra ->  Radicals -> SOLUTION: Question- How can you write the expression with rationalized denominator? 2 plus square root of 3 (with index root of 3) over square root of 6 also with index root of 3      Log On


   

Question 390898: Question- How can you write the expression with rationalized denominator?
2 plus square root of 3 (with index root of 3) over square root of 6 also with index root of 3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Broot%283%2C+3%29%29%2Froot%283%2C+6%29
BTW: These are called cube (or third) roots, not "square roots with index root of 3".

To rationalize the denominator we need to turn it into a cube root of a perfect cube. And we can change the denominator by multiplying the numerator and denominator by the same number. So we need to find the right number that will turn root%283%2C+6%29 into the cube root of a perfect cube. For this we can use root%283%2C+6%29%2Aroot%283%2C+6%29+=+root%283%2C+36%29:

In the numerator we use the Distributive Property. The denominators are easy to multiply:

which simplifies as follows:
%282%2Aroot%283%2C+36%29%2Broot%283%2C+108%29%29%2Froot%283%2C+216%29
%282%2Aroot%283%2C+36%29%2Broot%283%2C+108%29%29%2F6
%282%2Aroot%283%2C+36%29%2Broot%283%2C+27%2A4%29%29%2F6
%282%2Aroot%283%2C+36%29%2Broot%283%2C+27%29%2Aroot%283%2C+4%29%29%2F6
%282%2Aroot%283%2C+36%29%2B+3%2Aroot%283%2C+4%29%29%2F6
This is the simplified expression with a rational denominator.