ПОМОГИТЕ,СРОЧНО ПО МАТЕМАТИКЕЕЕ
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1) Сначала упростим отдельно корень 6-й степени:
2) А теперь работаем со всем выражением:
Ответ: 0.
![\sqrt[6]{25+4\sqrt{6}}=\sqrt[6]{24+1+4\sqrt{6}}=\sqrt[6]{4*6+4\sqrt{6}+1}=\sqrt[6]{(2\sqrt{6})^2+4\sqrt{6}+1}= \sqrt[6]{(2\sqrt{6})^2+2*2\sqrt{6}*1+1}= \sqrt[6]{(2\sqrt{6}+1)^2}= \sqrt[3]{2\sqrt{6}+1}= \sqrt[3]{1+2\sqrt{6}}](https://tex.z-dn.net/?f=+%5Csqrt%5B6%5D%7B25%2B4%5Csqrt%7B6%7D%7D%3D%5Csqrt%5B6%5D%7B24%2B1%2B4%5Csqrt%7B6%7D%7D%3D%5Csqrt%5B6%5D%7B4%2A6%2B4%5Csqrt%7B6%7D%2B1%7D%3D%5Csqrt%5B6%5D%7B%282%5Csqrt%7B6%7D%29%5E2%2B4%5Csqrt%7B6%7D%2B1%7D%3D+%5Csqrt%5B6%5D%7B%282%5Csqrt%7B6%7D%29%5E2%2B2%2A2%5Csqrt%7B6%7D%2A1%2B1%7D%3D+%5Csqrt%5B6%5D%7B%282%5Csqrt%7B6%7D%2B1%29%5E2%7D%3D+%5Csqrt%5B3%5D%7B2%5Csqrt%7B6%7D%2B1%7D%3D+%5Csqrt%5B3%5D%7B1%2B2%5Csqrt%7B6%7D%7D++ "\sqrt[6]{25+4\sqrt{6}}=\sqrt[6]{24+1+4\sqrt{6}}=\sqrt[6]{4*6+4\sqrt{6}+1}=\sqrt[6]{(2\sqrt{6})^2+4\sqrt{6}+1}= \sqrt[6]{(2\sqrt{6})^2+2*2\sqrt{6}*1+1}= \sqrt[6]{(2\sqrt{6}+1)^2}= \sqrt[3]{2\sqrt{6}+1}= \sqrt[3]{1+2\sqrt{6}}")
![(\sqrt[6]{25+4\sqrt{6}}-\sqrt[3]{1+2\sqrt{6}}) *\sqrt[3]{1-2\sqrt{6}} = (\sqrt[3]{1+2\sqrt{6}}-\sqrt[3]{1+2\sqrt{6}}) *\sqrt[3]{1-2\sqrt{6}} = 0*\sqrt[3]{1-2\sqrt{6}} = 0](https://tex.z-dn.net/?f=++%28%5Csqrt%5B6%5D%7B25%2B4%5Csqrt%7B6%7D%7D-%5Csqrt%5B3%5D%7B1%2B2%5Csqrt%7B6%7D%7D%29+%2A%5Csqrt%5B3%5D%7B1-2%5Csqrt%7B6%7D%7D++%3D++++%28%5Csqrt%5B3%5D%7B1%2B2%5Csqrt%7B6%7D%7D-%5Csqrt%5B3%5D%7B1%2B2%5Csqrt%7B6%7D%7D%29+%2A%5Csqrt%5B3%5D%7B1-2%5Csqrt%7B6%7D%7D++%3D+++0%2A%5Csqrt%5B3%5D%7B1-2%5Csqrt%7B6%7D%7D++%3D++0+++ "(\sqrt[6]{25+4\sqrt{6}}-\sqrt[3]{1+2\sqrt{6}}) *\sqrt[3]{1-2\sqrt{6}} = (\sqrt[3]{1+2\sqrt{6}}-\sqrt[3]{1+2\sqrt{6}}) *\sqrt[3]{1-2\sqrt{6}} = 0*\sqrt[3]{1-2\sqrt{6}} = 0")