Question

Найдите значение выражения 
$sqrt{4 m^{2}}- sqrt[3]{64 m^{3}}- sqrt[4]{625 m^{4}}+ sqrt[6]{727}$
при $m= sqrt[6]{727} -3$

Answer 1

$sqrt{4m^2}-sqrt[3]{64m^3}-sqrt[4]{625m^4}+sqrt[6]{727}=2|m|-4m-5|m|+sqrt[6]{727}=\ \ =-3|m|-4m+sqrt[6]{727}$

$sqrt[6]{727}~~ ?~~ 3~~~Rightarrow~~~ 727~~?~~3^6~~~Rightarrow~~~727 >729~~~Rightarrow~~ sqrt[6]{727}-3<0$

Если $m=sqrt[6]{727}-3$, то

$-3|m|-4m+sqrt[6]{727}=-3cdot (-(sqrt[6]{727}-3))-4(sqrt[6]{727}-3)+sqrt[6]{727}=\ \=3sqrt[6]{727}-9-4sqrt[6]{727}+12+sqrt[6]{727}=3$