Question

The value of $(127{)}^{1/3}$ to four decimal places is

• A. 5.0267
• B. 5.4267
• C. 5.5267
• D. 5.001

Answer 1

The correct option is A

5.0267

Let y = $x^{1/3},x=125$ and $x+\Delta x=127.$ Then,
$\frac{dy}{dx}=\frac{1}{3x^{2/3}}and\Delta x=0$
When, x = 125, we have
$y=5and\frac{dy}{dx}=\frac{1}{75}$
$\therefore y=\frac{dy}{dx}\Delta x\Rightarrow \Delta y\frac{1}{75}\times 2=\frac{2}{75}$
$\therefore (127{)}^{1/3}=y+\Delta y=5+\frac{2}{75}=5+\frac{8}{3}\times \frac{1}{100}$
$\Rightarrow (127{)}^{1/3}=5+\frac{\left(2.6667\right)}{100}=5.02667=5.0267$
Hence (a) is the correct answer.