Find the approximate value of 64.1. - Vidyadip

Question

Find the approximate value of $\sqrt{64.1}$.

✓

Answer

Let $f(x)=\sqrt{x}$
Differentiate w.r. $t . x$.
$f^{\prime}(x)=\frac{1}{2 \sqrt{x}}$
Let $a=64, h=0.1$
For $x=a=64$, from (I) we get
$f(a)=f(64)=\sqrt{64}=8$
For $x=a=64$, from (II) we get
$f^{\prime}(a)=f^{\prime}(64)=\frac{1}{2 \sqrt{64}}=\frac{1}{16}$
$\therefore \quad f^{\prime}(a)=0.0625$
We have, $f(a+h) \doteqdot f(a)+h f^{\prime}(a)$
$f(64+0.1) \doteqdot f(64)+(0.1) \cdot f^{\prime}(64)$
$f(64.1) \doteqdot 8+(0.1) \cdot(0.0625) \ldots$
[From (III) and (IV)]
$
\doteqdot 8+0.00625
$
$\therefore f(64.1)=\sqrt{64.1} \doteqdot 8.00625$

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