SOLUTION: Hi, What is the reciprocal of the (cube root of 81)? So if drawn out, it would have 3 as the index, and 81 as the radicand. Thanks!

Algebra ->  Radicals -> SOLUTION: Hi, What is the reciprocal of the (cube root of 81)? So if drawn out, it would have 3 as the index, and 81 as the radicand. Thanks!       Log On


   

Question 881765: Hi,
What is the reciprocal of the (cube root of 81)?
So if drawn out, it would have 3 as the index, and 81 as the radicand.
Thanks!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First simplify


root%283%2C81%29+=+root%283%2C27%2A3%29


root%283%2C81%29+=+root%283%2C27%29%2Aroot%283%2C3%29


root%283%2C81%29+=+3%2Aroot%283%2C3%29


-------------------------------------------------------


Then take the reciprocal. Make sure to rationalize the denominator.


1%2F%28root%283%2C81%29%29+=+1%2F%283%2Aroot%283%2C3%29%29


Multiply top and bottom by 2 copies of root%283%2C3%29 to rationalize the denominator.


1%2F%28root%283%2C81%29%29+=+%28root%283%2C3%2A3%29%29%2F%283%2Aroot%283%2C3%2A3%2A3%29%29


1%2F%28root%283%2C81%29%29+=+%28root%283%2C9%29%29%2F%283%2Aroot%283%2C27%29%29


1%2F%28root%283%2C81%29%29+=+%28root%283%2C9%29%29%2F%283%2A3%29


1%2F%28root%283%2C81%29%29+=+%28root%283%2C9%29%29%2F%289%29


-------------------------------------------------------


So the reciprocal of root%283%2C81%29 is %28root%283%2C9%29%29%2F%289%29