\[3\sqrt{1\frac{9}{16}} - 1 = 3\sqrt{\frac{25}{16}} - 1 =\]
\[= 3 \cdot \frac{5}{4} - 1 = \frac{15}{4} - 1 =\]
\[= 3\frac{3}{4} - 1 = 2\frac{3}{4}.\]