Explanation

As given that, $A = 1.0m \pm 0.2m$, $B = 2.0m \pm 0.2m$ So, $X = \sqrt{AB} = \sqrt{(1.0)(2.0)} = 1.414m$. Rounding off upto two significant digit $X = 1.4m = (r)$ (Let) $\Delta x/x = (1/2)[\Delta A/A + \Delta B/B] = (1/2)[0.2/1.0 + 0.2/2.0] \Rightarrow \Delta x = 0.6x/(2 \times 2.0) = (0.6 \times 1.4)/(2 \times 2.0) = 0.212$ Rounding off upto one significant digit $\Delta x = 0.2m = \Delta r$ (Let). So, correct value of $\sqrt{AB} = r + \Delta r = (1.4 \pm 0.2)m$