Which of these numbers does not have a square root of the form $x + y\sqrt{2}$?

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Which of the following numbers does not have a square root in the form \(x + y\sqrt{2}\), where \(x\) and \(y\) are positive integers?

1. \(17+12\sqrt{2}\)
2. \(22+12\sqrt{2}\)
3. \(38+12\sqrt{2}\)
4. \(54+12\sqrt{2}\)
5. \(73+12\sqrt{2}\)