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  "body": "\n## Statement\n\nLet $x$ be a real number, let $n$ be a positive integer and let $m$ be an [[integer|0C4JS9RF5M]] with $x^n = m$.\nIf $x$ is not an integer, then $x$ is [[irrational|080T2TXVQV]].\n\n## Remarks\n\nThus, a rational number $x$ with $x^n \\in \\mathbb{Z}$ is an integer.\nFor example, $\\sqrt[3]{2}$ is irrational, because $1^3 \u003c 2 \u003c 2^3$ shows that it is not an integer.\nThe statement follows from the rational root theorem for the polynomial $X^n - m$.\n\n## Explanations\n\n### L1 human\n\nTake a root of a whole number, for example $\\sqrt{10}$ or $\\sqrt[3]{20}$.\nEither the root is a whole number, as for $\\sqrt{9} = 3$, or it is not a fraction at all.\nA root of a whole number is never a fraction like $5/2$.\n",
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