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?
  1. 14.1608
  2. 14.0168
  3. 14.1086
  4. 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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