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√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.

See The Solution Submitted by Ady TZIDON    
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Solution 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
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