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(kommutativa lagen under addition) |
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(kommutativa lagen under multiplikation) |
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(associativa lagen under addition) |
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(associativa lagen under multiplikation) |
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(distributiva lagen) |
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(annulleringslagen under addition) |
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(annulleringslagen under multiplikation) |
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Låt
och
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(första kvadreringsregeln) |
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(andra kvadreringsregeln) |
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(konjugatregeln) |
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(fakultet)
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(binomialteoremet)
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(multinomialteoremet)
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Rötterna till andragradsekvationen på formen
ges av:

då gäller


För
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![{\displaystyle {\sqrt[{n}]{ab}}={\sqrt[{n}]{a}}{\sqrt[{n}]{b}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1353fff48e55340a3a5dc341a24ef72a08138aaa) |
![{\displaystyle {\sqrt[{n}]{\frac {a}{c}}}={\frac {\sqrt[{n}]{a}}{\sqrt[{n}]{c}}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c0ed2b4e4058f49e5094baf51e83c82978c11b81) |
![{\displaystyle {\sqrt[{m}]{\sqrt[{n}]{a}}}={\sqrt[{mn}]{a}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4db496e33fe5fdd7413b08b97c96590c53a2c4d8) |
![{\displaystyle a{\sqrt[{n}]{b}}={\sqrt[{n}]{a^{n}b}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef7652353cf33ce6dcc3896b2f95f32eb67cd211) |
![{\displaystyle {\sqrt[{m}]{\sqrt[{n}]{a}}}={\sqrt[{n}]{\sqrt[{m}]{a}}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbc1f9c84fc3aad1c24a74bfcef05165b381ac17) |
![{\displaystyle {\sqrt[{nq}]{a^{mq}}}={\sqrt[{n}]{a^{m}}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/25ba9040b8adffde97a1546a38ad67f98576b885) |
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![{\displaystyle a^{m/n}=(a^{m})^{1/n}={\sqrt[{n}]{a^{m}}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ce67a9cab7228a56e7f6b83b7a9fe05624d0a54a) |
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För
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![{\displaystyle \log _{a}{\sqrt[{n}]{a}}={\frac {1}{n}}\log a\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbfa1ba4d0338699af33c990ddaa1ae9baffcfc9) |
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