Posted by Paula on .
True or False.
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,
There 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,
find the value of 7+2(52.3^2).

Algebra 
Steve,
why? Have you no calculator?