Areas of three adjacent faces of a cuboid are $A_1 = 66\text{ cm}^2$, $A_2 = 192\text{ cm}^2$, and $A_3 = 198\text{ cm}^2$.

Multiply the three areas and take the square root. Since $66 = 6 \times 11$, $192 = 3 \times 64$, and $198 = 18 \times 11$, the product is $(6 \times 11) \times (3 \times 64) \times (18 \times 11) = (6 \times 3 \times 18) \times (11^2) \times 64 = 324 \times 121 \times 64$. Taking the square root gives $18 \times 11 \times 8 = 1584$.

Students often try to solve for $l, w, h$ individually by setting up equations like $lw=66$, $wh=192$, $lh=198$, which is more time-consuming than using the direct product formula.

This concept is similar to finding the product of roots in quadratic equations or geometric mean problems in statistics.