Given,

$\text{6}\sqrt{\text{2}}\text{ + 14.275=? of\hspace{0.17em}196.35}$

It can also be approximated as

$\text{6}\sqrt{\text{2}}\text{ + 14=? of\hspace{0.17em}200}$

= 6×1.14+14=? of 200

= 6.84+14= ? of 200

= 20.84= ? of 200

= $\frac{20.84}{200}$

= $\frac{1}{9}\approx \frac{1}{8}$

Hence, option C is correct.