Question

The approximate value of $(0.007{)}^{\frac{1}{3}}$ is

• A. $\frac{21}{120}$
• B. $\frac{23}{120}$
• C. $\frac{29}{120}$
• D. $\frac{31}{120}$

Answer 1

The correct option is B $\frac{23}{120}$

Let $f\left(x\right)=x^{\frac{1}{3}}$
Now, $f(x+\delta )-f\left(x\right)=f^{\prime }\left(x\right).\delta x=\frac{\delta x}{3x^{\frac{2}{3}}}$
We may write 0.007 = 0.008 – 0.001
Taking x = 0.008 and $\delta x=-0.001$
We have,
$f\left(0.007\right)-f\left(0.008\right)=-\frac{0.001}{3(0.008{)}^{\frac{2}{3}}}$
or $f\left(0.007\right)-f\left(0.008\right)=-\frac{1}{120}$
$\therefore f\left(0.007\right)=f\left(0.008\right)-\frac{1}{120}$
$\Rightarrow (0.007{)}^{\frac{1}{3}}=\frac{23}{120}$