Question

Сравнить 1/9√2268 и 16√1/8

Answer 1

$\frac{1}{9}\sqrt{2268}=\sqrt{(\frac{1}{9})^{2}*2268}=\sqrt{\frac{1}{81}*2268}=\sqrt{28}\\\\16\sqrt{\frac{1}{8}}=\sqrt{16^{2}*\frac{1}{8}}=\sqrt{256*\frac{1}{8}}= \sqrt{32}\\\\\sqrt{28}<\sqrt{32}\Rightarrow\frac{1}{9}\sqrt{2268} <16\sqrt{\frac{1}{8} }$