Question

Find the approximate value of ${\left(0.009\right)}^{1/3}$.

• A. $0.208$
• B. $0.108$
• C. $0.205$
• D. $0.204$

Answer 1

The correct option is A $0.208$

Using first order approximation,
$f(x+\Delta x)=f\left(x\right)+f^{\prime }\left(x\right)\Delta x$
Here assume $f\left(x\right)=x^{1/3}\Rightarrow f^{\prime }\left(x\right)=\frac{1}{3}{x}^{-2/3}$
$\therefore (0.009{)}^{1/3}=(0.008+0.001{)}^{1/3}=(0.008{)}^{1/3}+\frac{1}{3}(0.008{)}^{-2/3}\times 0.001=0.208$