Answer:
Let \[x=0.04\] \[\Rightarrow \] \[x+\Delta x=0.037\] Then, \[\Delta x=0.037-0.040\] \[\Delta x=-\,0.003\] \[y={{x}^{1/2}}\] \[\Rightarrow \] \[{{(0.04)}^{1/2}}=0.2\] \[y={{x}^{1/2}}\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{1}{2\sqrt{x}}\] \[\Rightarrow \] \[\Delta y=\frac{\Delta x}{2\sqrt{x}}\] \[\Rightarrow \] \[\Delta y=\frac{-\,0.003}{2\sqrt{0.04}}\] \[=\frac{-\,0.003}{2\times 0.2}\] \[=\frac{-\,3}{4\times 100}\] \[=\frac{-\,0.75}{100}\] \[\Rightarrow \] \[\Delta y=-\,0.0075\] \[y+\Delta y=0.2-0.0075\] = 0.1925 \[\therefore \] \[\sqrt{0.037}=0.1925\]
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