All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
√22 (Posted on 2017-10-18) Difficulty: 4 of 5
It easy to show that √2 is an irrational number

So is the square root of any non-square number.

Prove that √22 is an irrational number, providing a reasoning applicable to any random-chosen non-square integer.

  Submitted by Ady TZIDON    
No Rating
Solution: (Hide)
Sqrt(k) is rational iff it equals a/b, where a and b are integers.
Then k =a^2/b^2
and k*b^2 = a^2.
This is only possible if integer k is also square.
Therefore, sqrt(k) is rational iff the integer k is a square.

**Steve Herman's concised, slightly edited, solution.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionshort general proofCharlie2017-10-18 15:28:53
Slightly longer proofJayDeeKay2017-10-18 13:19:38
SolutionDon't be square (spoiler)Steve Herman2017-10-18 12:26:50
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information