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Because you are squaring numbers, the only way to get double is by using the square root of 2 which is 1.414.

A good example of this is paper sizes.

A4 is 210x297

A3 is double the size of A4 but to get that you need to multiply the sides by 1.414. That gives 297x420

But if you double each side of A4 you get 420x594 which is A2 and that is 4 times as big as A4 not 2 times as big.

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Take a look at the corresponding square roots (of the square numbers). If n^2 is a perfect square (the square of "n" - note: using "^" for exponentiation), then twice that number is the 2n^2. The square root of that is root(2) x n. And since root(2) (the square root of 2) is irrational, it follows that root(2) x n is not a whole number.

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9y ago
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Q: Why cant you find a square number which is double another?
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