Given,

$\begin{array}{l}\sqrt{\text{598746}}_3\text{ =?}\end{array}$

It can be approximated as

$$\begin{gathered} \sqrt[3]{600000} \\ \begin{array}{l}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}?=}\sqrt{600\times 1000}_3=\sqrt{512\times 1000}_3\end{array} \\ \begin{array}{l}?=\sqrt{8\times 8\times 8\times 10\times 10\times 10}_3\\ \downarrow \downarrow \\ 810\end{array} \end{gathered}$$

= 8×10

= 80 ≈ 84

Hence, Option C is correct.