Wednesday

October 7, 2015
Posted by **Paula** on Friday, July 26, 2013 at 12:44am.

The fifth root of a positive integer is sometimes irrational. Please give an example or a counterexample so that I can understand it fully.

- Algebra -
**Steve**, Friday, July 26, 2013 at 4:31amThere is no counterexample. The fifth root is indeed sometimes irrational.

Pick any integer which is not a perfect 5th power, and its 5th root is irrational.

5th powers: 0,1,32,343,1024,3125,...

These all have rational 5th roots: 0,1,2,3,4,5,...

Any numbers in between those have irrational 5th roots.

Not only is the 5th root sometimes irrational, it is "almost always" irrational. And yet, infinity is a strange animal. While it seems like the vast majority of integers ought to have irrational 5th roots, there are just as many which have rational 5th roots.

- Algebra -
**Anonymous**, Friday, July 26, 2013 at 8:37amfind the value of 7+2(5-2.3^2).

- Algebra -
**Steve**, Friday, July 26, 2013 at 1:52pmwhy? Have you no calculator?