We need to calculate the (1) expression with three significant figures. To simplify the division, we should find an expression in the form of (2) - that is, such coefficients $A, B, C$ - so that by extending (1) with it, we get a rational denominator. (The function table can be used.)

$$
\begin{gathered}
529 \\
\hline 12 \sqrt[3]{9}+52 \sqrt[3]{3}+49 \\
A \sqrt[3]{9}+B \sqrt[3]{3}+C
\end{gathered}
$$
(1) the product of the denominators and (2) - where possible, extracting the cube root from the $3^{3}$ factor -

$$
(49 A+52 B+12 C) \sqrt[3]{9}+(36 A+49 B+52 C) \sqrt[3]{3}+(156 A+36 B+49 C)
$$

This is certainly a rational number if the coefficients of $\sqrt[3]{9}$ and $\sqrt[3]{3}$ are 0, and the third term is rational. This is satisfied if the first two conditions can be met with rational $A, B, C$. From the requirements

$$
49 A+52 B+12 C=0 \quad 36 A+49 B+52 C=0
$$

treating $C$ as a parameter, we get $A=4 C, B=-4 C$, so choosing $C=1$ gives $A=4, B=-4$, and the value of the extended denominator is $156 \cdot 4-36 \cdot 4+49=529$. This is precisely the numerator of (1), so simplifying with this, the value of (1) is exactly the determined value of (2), which can be further transformed as follows:

$$
x=4 \sqrt[3]{9}-4 \sqrt[3]{3}+1=(2 \sqrt[3]{3}-1)^{2}=(\sqrt[3]{24}-1)^{2}
$$

According to the table, to 4 significant figures $\sqrt[3]{24}-1 \approx 1.884$, thus

$$
1.8835 \\
>3.5494-0.0020=3.5474>3.545
\end{gathered}
$$

and similarly

$$
1.8845^{2}<3.5495+0.0020<3.555
$$

therefore, rounding to 3 significant figures, $x \approx 3.55$.

Élthes Eszter (Budapest, I. István g. II. o. t.) Losonci Zoltán (Szeged, Vedres I. t. III. o. t.)