Question

The approximate value of $\sqrt[5]{533}$ correct to $4$ decimal places is

• A. $2.0000$
• B. $2.1001$
• C. $2.0125$
• D. $2.0500$

Answer 1

The correct option is C $2.0125$

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