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 $$1. \sqrt[n]{a^m} = a^{m\over n}$$ $$2. \sqrt[n]{a_1}*\sqrt[n]{a_2}*...*\sqrt[n]{a_k} = \sqrt[n]{a_1*a_2*...*a_k}$$ $$3. (\sqrt[n]{a})^m = \sqrt[n]{a^m}$$ $$4. {\sqrt[n]{a}\over\sqrt[n]{b}} = \sqrt[n]{a\over b}$$ $$5. \sqrt[n]{a} * \sqrt[m]{a} = \sqrt[nm]{a^{n+m}}$$ $$6. \sqrt[n]{\sqrt[m]{a}} = \sqrt[nm]{a} = \sqrt[m]{\sqrt[n]{a}}$$ $$7. \sqrt[n]{a^p} * \sqrt[m]{b^k} = \sqrt[nm]{a^{pm} * b^{kn}}$$ $$8. {\sqrt[n]{a^p}\over\sqrt[m]{b^k}} = \sqrt[nm]{a^{pm}\over b^{kn}}$$ $$9. (\sqrt[n]{a})^n = |a|$$ $$10. \sqrt[2n+1]{-a} = -\sqrt[2n+1]{a}$$ $$11. \sqrt{a} \pm \sqrt{b} = \sqrt{a\pm 2\sqrt{ab} + b}$$
 $$12. Scoaterea\hspace{3pt} factorilor\hspace{3pt} de\hspace{3pt} sub\hspace{3pt} radical : \sqrt[n]{a^{mn}*b^k} = a^m * \sqrt[n]{b^k}$$ $$13. Introducerea\hspace{3pt} factorilor\hspace{3pt} sub\hspace{3pt} radical : a^m * \sqrt[n]{b^k} = \sqrt[n]{a^{mn}*b^k}$$ $$14. "Amplificarea" radicalilor : \sqrt[n]{a^p} = \sqrt[nm]{a^{pm}}$$ $$15. Formula\hspace{3pt} radicalilor\hspace{3pt} compusi : \sqrt{A \pm \sqrt{B}} = \sqrt{A+C\over 2} \pm \sqrt{A-C\over 2} , unde\hspace{3pt} C = \sqrt{A^2 - B}$$ $$16. Pentru\hspace{3pt} \sqrt{a} \pm \sqrt{b}\hspace{3pt} expresia\hspace{3pt} conjugata\hspace{3pt} este : \sqrt{a} \mp \sqrt{b}$$ $$17. Pentru\hspace{3pt} \sqrt[3]{a} \pm \sqrt[3]{b}\hspace{3pt} expresia\hspace{3pt} conjugata\hspace{3pt} este : \sqrt[3]{b^2} \mp \sqrt[3]{ab} + \sqrt[3]{b^2}$$ $$\underline{Conditii\hspace{3pt} de\hspace{3pt} existenta} :$$ $$1. Pentru\hspace{3pt} radicali\hspace{3pt} de\hspace{3pt} ordin\hspace{3pt} par,\hspace{3pt} de\hspace{3pt} forma\hspace{3pt} \sqrt[2n]{E(x)},\hspace{3pt} se\hspace{3pt} va\hspace{3pt} pune,\hspace{3pt} obligatoriu,\hspace{3pt}$$ $$conditia\hspace{3pt} E(x)>=0$$ $$2. Pentru\hspace{3pt} radicali\hspace{3pt} de\hspace{3pt} ordin\hspace{3pt} impar,\hspace{3pt} de\hspace{3pt} forma\hspace{3pt} \sqrt[2n+1]{E(x)},\hspace{3pt} nu\hspace{3pt} se\hspace{3pt} pun\hspace{3pt} conditii\hspace{3pt} de\hspace{3pt} existenta\hspace{3pt} si,$$ $$ca\hspace{3pt} urmare,\hspace{3pt} x\hspace{3pt} poate\hspace{3pt} fi\hspace{3pt} orice\hspace{3pt} numar\hspace{3pt} real.$$