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Provide solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xxix)

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Answer: 0.2867

Hint: Here we use this below formula

        \Delta y=f(x+\Delta x)-f(x)

Given: \sqrt{0.082}

Solution: \text { let } f(x)=\sqrt{x}

Using f(x+\Delta x)=f(x)+\Delta x \times f(x)

Taking x=09 \text { and } \Delta x=-0.008

We get  f(0.09-0.008)=f(0.09)+(-0.008)(0.09)

\begin{aligned} &\Rightarrow \sqrt{0.082}=\sqrt{0.09}-0.0008 \times \frac{1}{2 \sqrt{0.09}} \\\\ &=0.3-\frac{0.008}{0.6} \\\\ &=0.3-0.01333=0.2867 \end{aligned}

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