Question

сравнить два выражения

Answer 1

$\displaystyle\bf\\1) \ \ 6\sqrt{\frac{2}{3} } =\sqrt{6^{2}\cdot\frac{2}{3} } =\sqrt{36\cdot\frac{2}{3} } =\sqrt{12\cdot 2}=\sqrt{24} } \\\\\\2) \ \ \frac{1}{2} \sqrt{88} =\sqrt{\Big(\frac{1}{2} \Big)^{2} \cdot88}=\sqrt{\frac{1}{4} \cdot88} =\sqrt{22} \\\\\\\sqrt{24} >\sqrt{22} \ \ \Rightarrow \ \ \boxed{6\sqrt{\frac{2}{3} } >\frac{1}{2} \sqrt{88}}$