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  "body": "\n## Statement\n\nLet $p$ be a prime number.\nThen $\\sqrt{p}$ is an [[irrational number|080T2TXVQV]].\n\n## Remarks\n\nThis generalizes the [[irrationality of the square root of 2|0DZGSDHD92]].\nMore generally, the square root of a natural number $n$ is irrational unless $n$ is a perfect square. See [[the roots of integers|0XWCKJZRYH]].\n\n## Explanations\n\n### L1 human\n\nThe numbers $\\sqrt{2}$, $\\sqrt{3}$, $\\sqrt{5}$ and $\\sqrt{7}$ are all irrational.\nThe proof for $\\sqrt{2}$ works for each prime: if $a^2 = p b^2$, then $p$ divides $a$, and then $p$ also divides $b$.\n",
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