Question

Ребята помогите ( степень корней

Answer 1

$\sqrt[8]{a^6}+\sqrt[6]{g^4}+\sqrt[12]{m^8}+\sqrt[24]{m^{16}}=\sqrt[4]{a^3}+\sqrt[3]{g^2}+\sqrt[3]{m^2}+\sqrt[3]{m^{2}}$

$\sqrt[2]{a^2b^4}+\sqrt[3]{a^3b^6}+\sqrt[4]{a^4b^8}-\sqrt[5]{a^5b^{15}}=ab^2+ab^2+ab^2-ab^3= \\ =3ab^2-ab^3$

$\sqrt[4]{6+2\sqrt5}*\sqrt[4]{6-2\sqrt5}=\sqrt[4]{(6+2\sqrt5)(6-2\sqrt5)}=\sqrt[4]{6^2-(2\sqrt5)^2}= \\ =\sqrt[4]{36-20}=\sqrt[4]{16}= =\sqrt[4]{2^4}= 2$

$\sqrt[3]{\sqrt{17}+3}*\sqrt[3]{\sqrt{17}-3}=\sqrt[3]{(\sqrt{17}+3)(\sqrt{17}-3)}=\sqrt[3]{(\sqrt{17}^2-9)}= \\ =\sqrt[3]{(17-9)}= \sqrt[3]{8}= \sqrt[3]{2^3}=2$