5root 75 +8 root 108-1by 2 root 48

The given question can be written in the Mathematical form as:

$$\begin{gathered} 5\sqrt{75}+8\sqrt{108}-\frac{1}{2\sqrt{48}} \\ =5\sqrt{25\times 3}+8\sqrt{36\times 3}-\frac{1}{2\sqrt{16\times 3}} \\ = 5\times 5\sqrt{3}+8\times 6\sqrt{3}-\frac{1}{2\times 4\sqrt{3}} \\ = 25\sqrt{3}+48\sqrt{3}-\frac{1}{8\sqrt{3}} \\ = \frac{25\sqrt{3}\times 8\sqrt{3}+48\sqrt{3}\times 8\sqrt{3}-1}{8\sqrt{3}} \\ = \frac{200\times 3+384\times 3-1}{8\sqrt{3}} \\ = \frac{600+1152-1}{8\sqrt{3}} \\ = \frac{1751}{8\sqrt{3}} \\ = \frac{1751}{8\sqrt{3}}\times \frac{8\sqrt{3}}{8\sqrt{3}} \\ = \frac{14008\sqrt{3}}{192} \\ = \frac{1751\sqrt{3}}{24} \end{gathered}$$