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  "body": "\n## Statement\n\nThe number $\\sqrt[3]{2}$ is not a [[constructible number|0FMN2MN7TM]].\nSo the cube cannot be [[doubled|04SD3F4FCR]] with straightedge and compass.\n\n## Remarks\n\nThe proof: $x^3 - 2$ is irreducible over $\\mathbb{Q}$, by [[Eisenstein's criterion|02BPKD7TMD]] with $p = 2$. So $[\\mathbb{Q}(\\sqrt[3]{2}) : \\mathbb{Q}] = 3$.\nSince $3$ is not a power of $2$, the number $\\sqrt[3]{2}$ is not constructible, by the [[degree theorem|0SSSM1D475]].\n\n## History\n\nPierre Wantzel proved the impossibility in 1837.\n\n## Explanations\n\n### L1 human\n\nThe edge of the doubled cube is the cube root of $2$.\nIts minimal polynomial has degree $3$, but constructible numbers have degree a power of $2$.\n",
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