Number Theory Help: Prove 5^(1/3) is irrational.
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Number Theory Help: Prove 5^(1/3) is irrational.

Number Theory Help: Prove 5^(1/3) is irrational.

[From: ] [author: ] [Date: 11-10-12] [Hit: ]
that 5 divides q, and hence derive a contradiction.......
Yes indeed -- the standard proof of the fact that 2^(1/2) can be mimicked to obtain this result.

Suppose that 5^(1/3) is rational: thus, we may write 5^(1/3) = p/q, where gcd(p, q) = 1. Then 5 = (p^3)/(q^3), or 5q^3 = p^3. Deduce that 5 divides p, that 5 divides q, and hence derive a contradiction.
1
keywords: Theory,Number,Help,Prove,irrational,is,Number Theory Help: Prove 5^(1/3) is irrational.
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .