Task B-1.2. Calculate:

$$
\sqrt{\frac{145.5^{2}-96.5^{2}}{193.5^{2}-31.5^{2}}}
$$
$$
\begin{aligned}
\sqrt{\frac{145.5^{2}-96.5^{2}}{193.5^{2}-31.5^{2}}} & =\sqrt{\frac{(145.5+96.5)(145.5-96.5)}{(193.5+31.5)(193.5-31.5)}}= \\
& =\sqrt{\frac{242 \cdot 49}{225 \cdot 162}}=\sqrt{\frac{121 \cdot 49}{225 \cdot 81}}=\frac{77}{135}
\end{aligned}
$$

Solution.

$$
\begin{aligned}
\sqrt{\frac{145.5^{2}-96.5^{2}}{193.5^{2}-31.5^{2}}} & =\sqrt{\frac{(145.5+96.5)(145.5-96.5)}{(193.5+31.5)(193.5-31.5)}}= \\
& =\sqrt{\frac{242 \cdot 49}{225 \cdot 162}}=\sqrt{\frac{121 \cdot 49}{225 \cdot 81}}=\frac{77}{135}
\end{aligned}
$$