Question

Сравните :
1) $sqrt{200}$ + $sqrt{200}$ ... $sqrt{400}$
2) 5$sqrt{27}$ + 2$sqrt{48}$ ... 9$sqrt{2}$
Знак ставить на место точек. Спасибо.

Answer 1

$sqrt{200}+sqrt{200}=sqrt{2}*sqrt{100}+sqrt{2}+sqrt{100}=sqrt{2}(sqrt{100}+sqrt{100})=20sqrt{2}\ sqrt{400}=20\ sqrt{200}+sqrt{200} textgreater sqrt{400}\ \ sqrt[5]{27}+sqrt{48} =sqrt[5]{3^3}+sqrt{3*16}=3^{frac{3}{5}}+4*3^{frac{1}2} textgreater 2\ sqrt[9]{2}=2^{frac{1}9} textgreater 2\ sqrt[5]{27}+sqrt{48} textgreater sqrt[9]{2}$