Solution:
$$\eqalign{ {\text{According to question,}} \cr \Rightarrow \sqrt {\frac{8}{3}} \cr \Rightarrow \sqrt {\frac{{8 \times 3}}{{3 \times 3}}} \cr \Rightarrow \sqrt {\frac{{24}}{9}} \cr \Rightarrow \frac{{4.898}}{3} \cr \Rightarrow 1.633 \cr} $$

Solution:
$$\eqalign{ {\text{Sum of given fractions}} \cr {\text{ = }}\frac{7}{4} + \frac{5}{2} + \frac{{67}}{{12}} + \frac{{10}}{3} + \frac{9}{4} \cr = \left( {\frac{{21 + 30 + 67 + 40 + 24}}{{12}}} \right) \cr = \frac{{185}}{{12}} \cr {\text{The whole number just }} \cr {\text{less than }}\frac{{185}}{{12}}{\text{ is 15}} \cr {\text{let }}\frac{{185}}{{12}} - x = 15 \cr {\text{Then,}} \cr x = \left( {\frac{{185}}{{12}} - 15} \right) \cr \,\,\,\,\,\, = \frac{5}{{12}} \cr} $$

Solution:
xyz = 256 ⇒ (2z) (2z) z = 256 ⇒ 4z³
= 256 ⇒ z³ = 64 ⇒ z = 4
∴ x = 2z = (2 × 4) = 8

Solution:
$$\eqalign{ {\text{According to question,}} \cr \frac{{3\frac{1}{4} - \frac{4}{5}{\text{ of }}\frac{5}{6}}}{{4\frac{1}{3} \div \frac{1}{5} - \left( {\frac{3}{{10}} + 21\frac{1}{5}} \right)}}{\text{ }} \cr \Rightarrow \frac{{\frac{{13}}{4} - \frac{4}{5} \times \frac{5}{6}}}{{\frac{{13}}{3} \times 5 - \left( {\frac{3}{{10}} + \frac{{106}}{5}} \right)}}{\text{ }} \cr \Rightarrow \frac{{\frac{{13}}{4} - \frac{2}{3}}}{{\frac{{65}}{3} - \frac{3}{{10}} - \frac{{106}}{5}}} \cr \Rightarrow \frac{{\frac{{39 - 8}}{{12}}}}{{\frac{{650 - 9 - 636}}{{30}}}} \cr \Rightarrow \frac{{31}}{{12}} \times \frac{{30}}{5} \cr \Rightarrow \frac{{31}}{2} \cr \Rightarrow 15\frac{1}{2} \cr} $$
∴ Least fraction number should be subtracted is:
$${\text{15}}\frac{1}{2} - 15 = \frac{1}{2}$$     (least fraction number)

Solution:
200 ÷ 25 × 4 + 12 - 3
= $$\frac{{200}}{{25}}$$ × 4 + 12 - 3
= 8 × 4 + 12 - 3
= 32 + 12 - 3
= 44 - 3
= 41

Solution:
$$\eqalign{ \frac{{\left( {\frac{2}{5}{\text{ of }}6\frac{1}{4} \div \frac{3}{7}} \right) \times 1\frac{2}{7}}}{{11\frac{1}{4}}} = \sqrt x \cr \frac{{\left( {\frac{2}{5}{\text{ of }}\frac{{25}}{4} \div \frac{3}{7}} \right) \times \frac{9}{7}}}{{\frac{{45}}{4}}} = \sqrt x \cr \frac{{\frac{5}{2} \times \frac{7}{3} \times \frac{9}{7}}}{{\frac{{45}}{4}}} = \sqrt x \cr \frac{{15}}{2} \times \frac{4}{{45}} = \sqrt x \cr x = \frac{4}{9} \cr 81x = 81 \times \frac{4}{9} \cr 81x = 36 \cr} $$

Solution:
$$\eqalign{ \frac{{1\frac{2}{3} \div \frac{5}{6} \times 6 + \frac{4}{5} \times \frac{1}{2} + \frac{2}{3}}}{{2 - \left[ {1\frac{1}{3} \times \left( { - \frac{3}{5}} \right) - 6\left\{ {\frac{3}{5} - \left( {3 - \frac{3}{{10}}} \right)} \right\}} \right]}} \cr = \frac{{\frac{5}{3} \times \frac{6}{5} \times 6 + \frac{4}{{10}} + \frac{2}{3}}}{{2 - \left[ {\frac{4}{3} \times \frac{{ - 3}}{5} - 6\left\{ {\frac{3}{5} - \frac{{27}}{{10}}} \right\}} \right]}} \cr = \frac{{12 + \frac{{6 + 10}}{{15}}}}{{2 - \left( { - \frac{4}{5} + \frac{{21 \times 6}}{{10}}} \right)}} \cr = \frac{{12 + \frac{{16}}{{15}}}}{{2 - \left( { - \frac{4}{5} + \frac{{63}}{5}} \right)}} \cr = \frac{{\frac{{196}}{{15}}}}{{2 - \frac{{59}}{5}}} \cr = \frac{{196}}{{15}} \times \frac{{ - 5}}{{49}} \cr = \boxed{ - \frac{4}{3}} \cr} $$