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√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

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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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