Friday

December 19, 2014

December 19, 2014

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?

**Answer this Question**

**Related Questions**

Algebra - A positive integer minus a positive integer is always positive. This ...

Math - Are these true or false? 1. If s is negative, then the square root of s^2...

math - 1. Which of the following numbers is an example of an integer? a. -15 b. ...

math - Algebra For questions 1-5, find the value of the variable. 1. x = (1 ...

Algebra II - In an induction proof of the statement 4+7+10+...+(3n-1)=n(3n+5)/2 ...

7th grade math Ms.Sue please - 1. Which of these numbers can be classified as ...

math - 1. Rosa, Roberto, Andrea, and Inno find an estimate for the square root ...

math - 1)Find the third iterate x3 of f(x)=x2-4 for an initial value of x0=2 A)-...

Math - When you add a positive integer and a negative integer, you sometimes get...

Math - Determine whether the statement is true, false, or sometimes true. ...