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Explain solution RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xix) maths

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Answer: 6.08

Hint: \Delta y=f(x+\Delta x)-f(x)

        Let's use this formula

Given: \sqrt{37}

Solution:  \frac{d y}{d x}=\frac{1}{2 \sqrt{x}}

So, we get

        \Delta y=\frac{d y}{d x} \Delta x

So , we get

        \Delta y=\frac{1}{2 \sqrt{x}} \times 1

on further calculation

        \Delta y=\frac{1}{12}=0.08

we know that

        \Delta y=f(x+\Delta x)-f(x)

By substituting the values,

        \begin{aligned} &0.08=\sqrt{36+1}-\sqrt{36} \\\\ &0.08=\sqrt{37}-6 \\\\ &\sqrt{37}=6.08 \end{aligned}


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