perplexus.info :: Numbers : √22

√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.

Submitted by Ady TZIDON

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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
short general proof	Charlie	2017-10-18 15:28:53
Slightly longer proof	JayDeeKay	2017-10-18 13:19:38
Don't be square (spoiler)	Steve Herman	2017-10-18 12:26:50

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