Question

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

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

Answer 1

Answer: (C)

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