331 x square-root[291/273]

331 √(291 / 273)
= 331 √(97 / 91)

since 9² = 81 and 10² = 100, so 9 < √97 < 10
since 9.5² = 90.25 and 10² = 100, so 9.5 < √97 < 10
since 9.75² = 95.06 and 10² = 100, so 9.75 < √97 < 10
since 9.75² = 95.06 and 9.875² = 97.52, so 9.75 < √97 < 9.875
since 9.8125² = 96.29 and 9.875² = 97.52, so 9.8125 < √97 < 9.875
since 9.84375² = 96.90 and 9.875² = 97.52, so 9.84375 < √97 < 9.875
since 9.84375² = 96.90 and 9.859375² = 97.21,
so 9.84375 < √97 < 9.859375
since 9.84375² = 96.90 and 9.8515625² = 97.05,
so 9.84375 < √97 < 9.8515625
since 9.84765625² = 96.98 and 9.8515625² = 97.05,
so 9.84765625 < √97 < 9.8515625
therefore, √97 approximately equal to 9.85 (cor. to 3 sig. fig)
Similarly, we have √91 approximately equal to 9.54 (cor. to 3 sig. fig)

thus, 331 √(291 / 273)
= 331 √(97 / 91)
≒ 331 x (9.85 / 9.54)
≒ 341.76

331 √(291 / 273)
= 331 √(97 / 91)
= 331 x (9.85 / 9.54)
= 341.76