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

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Answer: 5.03

Hint: Here we use the formula

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

Given: \sqrt{25.3}

Solution: let y=\sqrt{x}

\begin{aligned} &x=25 \& \Delta x=0.3 \\\\ &\Rightarrow \text { Since } y=\sqrt{x} \\\\ &\frac{d y}{d x}=\frac{d \sqrt{x}}{d x}=\frac{1}{2 \sqrt{x}} \end{aligned}

⇒ Now,

\begin{aligned} &\Delta y=\frac{d y}{d x} \Delta x \\\\ &=\frac{1}{2 \sqrt{x}} \times 0.3 \\\\ &=\frac{1}{2 \sqrt{x}} \times 0.3=0.03 \end{aligned}

\begin{aligned} &\Rightarrow \text { Also, } \Delta y= \frac{f(x+\Delta x)-f(x)}\ ={\sqrt{25+0.3}-\sqrt{25}} \\\\ &\sqrt{25.3}=5.03 \end{aligned}

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