SOLUTION: 1/ qube root of 3+1

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Question 895695: 1/ qube root of 3+1
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What? Which?

1%2Froot%283%2C3%29%2B1
Multiply only the first rational expression by %28root%283%2C3%29root%283%2C3%29%29%2F%28root%283%2C3%29root%283%2C3%29%29

1%2F%28root%283%2C3%29%2B1%29
A little trickier.
A very good piece of guidance is shown, here:
http://www.purplemath.com/modules/radicals7.htm

OR still, you you mean,
1%2Froot%283%2C3%2B1%29
?


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If your expression is the first one or the last one, then rationalizing the denominator is very simple.

IF you have THIS ONE, highlight_green%281%2F%28root%283%2C3%29%2B1%29%29, then this is how and what to know:

Polynomial division of a%5E3%2Bb%5E3 by a%2Bb will give the quotient, a%5E2-ab%2Bb%5E2.

Starting with 1%2F%28root%283%2C3%29%2B1%29 and using root%283%2C3%29=a and 1=b, rationalize the denominator
through multiplication of the expression by 1.

This 1 uses %28root%283%2C3%29%29%5E2-root%283%2C3%29%2B1 in numerator and denominator.





%28%28root%283%2C3%29%29%5E2-root%283%2C3%29%2B1%29%2F%283%2B1%29

highlight%28%28%28root%283%2C3%29%29%5E2-root%283%2C3%29%2B1%29%2F4%29