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Q. The approximate value of $\sqrt[5]{33}$ correct to $4$ decimal places is

WBJEEWBJEE 2011Application of Derivatives

Solution:

Let $f(x)=x^{1 / 5}$
$=(32+1)^{1 / 5}$
Here, $ a=32, h=\frac{1}{5}, $
$\therefore f(a+b) =f(a)+h f^{\prime}(a)$
$ \therefore (32+1)^{1 / 5} =(32)^{1 / 5}+\frac{1}{5} \times \frac{1}{(32)^{4 / 5}} $
$=2+\frac{1}{80}=2+0.0125 $
$=2.0125$