The approximate value of (33)^ 1 5 is:

MCQ

The approximate value of $(33)^{\frac{1}{5}}$ is:

✓
$2.0125$
B
$2.1$
C
$2.01$
D
None of these

✓

Answer

Correct option: A.

$2.0125$

To find $(33)^{\frac{1}{5}}$ we consider $\text{f(x)}=\text{x}^{\frac{1}{5}}$
Here$, x = 32,$
$\triangle\text{x}=1$
$\text{f}(32)=32^{\frac{1}{5}}=2$
$\Rightarrow\text{f}\ '(\text{x})=\frac{1}{5}\times\frac{-4}{5}$
$\Rightarrow\text{f}\ '(32)=\frac{1}{5}(32)^{\frac{-4}{5}}=\frac{1}{80}$
$\triangle\text{y}=\frac{\text{dy}}{\text{dx}}\text{dx}=0.0125$
$\Rightarrow\text{f}(33)=2+0.0123=2.0125$

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