perplexus.info :: Numbers : √22

Home > Numbers

√22 (Posted on 2017-10-18)

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.

See The Solution Submitted by Ady TZIDON

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Don't be square (spoiler)

| Comment 1 of 3

sgrt(k) is rational if and only if 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, sgrt(k) is rational if and only integer k is a square.

Posted by Steve Herman on 2017-10-18 12:26:50

Please log in:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (24)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info