\[\boxed{\text{415\ (415).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ \frac{1}{3}\sqrt{351} < \frac{1}{2}\sqrt{188}\]
\[\sqrt{\frac{1}{9} \cdot 351} < \sqrt{\frac{1}{4} \cdot 188}\]
\[\sqrt{39} < \sqrt{47}\]
\[\textbf{б)}\ \frac{1}{3}\sqrt{54} = \frac{1}{5}\sqrt{150}\]
\[\sqrt{\frac{1}{9} \cdot 54} = \sqrt{\frac{1}{25} \cdot 150}\]
\[\sqrt{6} = \sqrt{6}\]
\[\textbf{в)}\ \sqrt{24} = \frac{1}{3}\sqrt{216}\]
\[\sqrt{24} = \sqrt{\frac{1}{9} \cdot 216}\]
\[\sqrt{24} = \sqrt{24}\]
\[\textbf{г)}\frac{2}{3}\sqrt{72} < 7\sqrt{\frac{2}{3}}\]
\[\sqrt{\frac{4}{9} \cdot 72} < \sqrt{49 \cdot \frac{2}{3}}\]
\[\sqrt{32} < \sqrt{\frac{98}{3}} = \sqrt{32\frac{2}{3}}\]