Question

Simplify:

$\frac{4}{5}\mathrm{of}\frac{205}{64}\times 7\left[\sqrt{256}÷32\left\{77+\overline{12-3}\left(\sqrt{49}+5\right)\right\}\right]$

Answer 1

Simplify the given expression

$$\begin{gathered} \frac{4}{5}\mathrm{of}\frac{205}{64}\times 7\left[\sqrt{256}÷32\left\{77+\overline{12-3}\left(\sqrt{49}+5\right)\right\}\right]=\frac{4}{5}of\frac{205}{64}\times 7\left[\sqrt{256}÷32\left\{77+9\left(\sqrt{49}+5\right)\right\}\right] \\ =\frac{4}{5}of\frac{205}{64}\times 7\left[\sqrt{256}÷32\left\{77+9\left(7+5\right)\right\}\right] \\ =\frac{4}{5}of\frac{205}{64}\times 7\left[16÷32\left\{77+9\times 12\right\}\right] \\ =\frac{4}{5}of\frac{205}{64}\times 7\left[16÷32\left\{77+108\right\}\right] \\ =\frac{4}{5}of\frac{205}{64}\times 7\left[16÷32\times 185\right] \\ =\frac{4}{5}of\frac{205}{64}\times 7\left[\frac{16}{32}\times 185\right] \\ =\frac{4}{5}of\frac{205}{64}\times 7\times \left[\frac{1}{2}\times 185\right] \\ =\frac{41}{16}\times 7\times \frac{1}{2}\times 185 \\ =\frac{287}{32}\times 185 \\ =\frac{53095}{32} \end{gathered}$$

Hence, the required answer is $\frac{53095}{32}$.