\[\sqrt{1,5} = \sqrt{1\frac{1}{2}} = \sqrt{1\frac{3}{6}};\ \]
\[\text{\ \ }\sqrt{1\frac{2}{3}} = \sqrt{1\frac{4}{6}}\]
\[\Longrightarrow \sqrt{1,5} < \sqrt{1\frac{2}{3}}.\]