Question

The approximate value of $(33{)}^{1/5}$ is

• A. 2.0125
• B. 2.1
• C. 2.01
• D. none of these

Answer 1

Answer: (A)

2.0125

$(33{)}^{1/5}=(32+1{)}^{1/5}$
Let $y=f\left(x\right)=x^{1/5}$
$\Rightarrow y+\Delta y=(x+\Delta x{)}^{1/5}$
$\Rightarrow \Delta y=(x+\Delta x{)}^{1/5}-x^{1/5}$
Also, $\Delta y=f^{\prime }\left(x\right)\Delta x$
$\Rightarrow (x+\Delta x{)}^{1/5}-x^{1/5}=\frac{1}{5}{x}^{-4/5}\Delta x$
Put $x=32,\Delta x=1$
$(33{)}^{1/5}-(32{)}^{1/5}=\frac{1}{5}\left(2{)}^{-4}\right(1)$
$\Rightarrow (33{)}^{1/5}=2+0.0125=2.0125$