What is an approximate value of $\sqrt{199}$ corrected to 4 decimal places?
What is an approximate value of $\sqrt{199}$ corrected to 4 decimal places?
- 14.1608
- 14.0168
- 14.1086
- 14.1071
Solution
Let a function $f(x)=\sqrt{x}$
and $\quad x=196$ and $\Delta x=3$
$
\begin{aligned}
\because \quad \Delta y & =\left.\frac{d y}{d x}\right|_{x=196} \times \Delta x \\
& =\left.\frac{1}{2 \sqrt{x}}\right|_{x=196} \times 3=\frac{3}{28}=0.1071 \\
\therefore \quad \sqrt{199} & =14+01071=14.1071
\end{aligned}
$
Asked in: AP EAMCET 2020 (22 Sep Shift 1)
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