KöMaL 2020 B5106

The numbers $n+1, n+2, \ldots, 2n$ are written on a blackboard ($n\ge2$), and the following procedure is repeated: two numbers are selected ($x$ and $y$) from the board, erased, and replaced with the numbers $x+y+\sqrt{x^2+y^2}$ and $x+y-\sqrt{x^2+y^2}$. Prove that there will never be a number less than 1.442 written on the board.