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Please solve RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xxiv) maths textbook solution

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Answer: 6.05

Hint: Here we use this below formula

        \Delta y=f(x+\Delta x)-f(x)

Given: \sqrt{36.6}

Solution: y=\sqrt{x} \text { let } x=36 \text { and } A x=0.6 then,

        \begin{aligned} &\Delta y=\sqrt{x+\Delta x}-\sqrt{x} \\\\ &=\sqrt{36.6}-\sqrt{36} \\\\ &=\sqrt{36.6}-6 \\\\ &\Delta y=\sqrt{36.6}-6 \end{aligned}

now,  dy is approximate equal to  Ay and is given by.

        \begin{aligned} &d y=\left(\frac{d y}{d x}\right) d x=\frac{1}{2 \sqrt{x}}(0.6) \\\\ &\frac{1}{2 \sqrt{36}} \times 0.6=0.05 \end{aligned}

The approximate value of \sqrt{36.6} \text { is } 6+0.05=6.05

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