You measure two quantities as $A=1.0m\pm 0.2m,B=0.2m\pm 0.2m.$ We should report correct value for $\sqrt{AB}$ is

Given $A=1.0m\pm 0.2m$

$B=2.0m\pm 0.2m$

$x=\sqrt{AB}=\sqrt{1.0\times 2.0}=1.414m$

Rounding-off to two significant digits,

$x=\sqrt{AB}=1.4m$

Now, $\frac{\Delta x}{x}=\frac{1}{2}[\frac{\Delta A}{A}+\frac{\Delta B}{B}]$

$=\frac{1}{2}[\frac{0.2}{1.0}+\frac{0.2}{0.2}]=\frac{0.6}{2\times 2.0}$

$\Delta x=\frac{0.6\times x}{2\times 2.0}=0.15\times 1.414=0.2121$

Rounding-off to one significant digits, $\Delta x=0.2m$

Thus, $\sqrt{AB}=1.4m\pm 0.2m$