SOLUTION: i took a test and scored low , but a question that am not sure about is when my professor asked " what should I multiply 2/cube 2x square by,to rationalize the denominator? the ans

Algebra ->  Square-cubic-other-roots -> SOLUTION: i took a test and scored low , but a question that am not sure about is when my professor asked " what should I multiply 2/cube 2x square by,to rationalize the denominator? the ans      Log On


   

Question 189564: i took a test and scored low , but a question that am not sure about is when my professor asked " what should I multiply 2/cube 2x square by,to rationalize the denominator? the answer is cube 4x Why isnt it 8 cube x
thank and have nice day jay


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
One thing to note: root%283%2C4x%29=root%283%2C2x%2A2x%29=root%283%2C2x%29root%283%2C2x%29


2%2Froot%283%2C2x%29 Start with the given expression.


To rationalize the denominator, we need the denominator to be the cube root of something cubed (so the cube root would cancel out). So we need 3 instances of 2x to get %282x%29%5E3. This is why we multiply both the numerator and denominator by root%283%2C2x%29root%283%2C2x%29 (add these to the original root to get 3 roots)



Multiply both the numerator and denominator by root%283%2C2x%29root%283%2C2x%29


%282%2Aroot%283%2C2x%2A2x%29%29%2F%28root%283%2C2x%2A2x%2A2x%29%29 Combine the roots.


%282%2Aroot%283%2C%282x%29%5E2%29%29%2F%28root%283%2C%282x%29%5E3%29%29 Condense the terms.


%282%2Aroot%283%2C%282x%29%5E2%29%29%2F%282x%29 Take the cube root of the cube in the denominator to cancel out the cube root. The denominator is now rationalized.