Physics - Error Question with Solution | TestHub

Given, $A=1.0\mathrm{m}\pm 0.2\mathrm{m},B=2.0\mathrm{m}\pm 0.2\mathrm{m}$ Let $Y=\sqrt{AB}=\sqrt{(1.0)(20)}=1.414\mathrm{m}$ Rounding off to two significant digits $\begin{array}{rl}Y& =1.4\mathrm{m}\\ \frac{\Delta Y}{Y}& =\frac{1}{2}\left[\frac{\Delta A}{A}+\frac{\Delta B}{B}\right]\\ & =\frac{1}{2}\left[\frac{0.2}{1.0}+\frac{0.2}{2.0}\right]\\ & =\frac{0.6}{2\times 20}\\ \Rightarrow \Delta Y& =\frac{0.6Y}{2\times 20}=\frac{0.6\times 1.4}{2\times 20}=0.212\end{array}$ Rounding off to one significant digit, $\Delta Y=0.2\mathrm{m}$