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

5.0267

Let $y=x^{1 / 3}, x=125$ and $x+\Delta x=127$. Then, $\frac{d y}{d x}=\frac{1}{3 x^{2 / 3}}$ and $\Delta x=2$

When, $x=125$, we have

$y=5 \text { and } \frac{d y}{d x}=\frac{1}{75}$

∴  $\Delta y=\frac{d y}{d x} \Delta x \Rightarrow \Delta y=\frac{1}{75} \times 2=\frac{2}{75}$

∴  $(127)^{1 / 3}=y+\Delta y=5+\frac{2}{75}=5+\frac{8}{3} \times \frac{1}{100}$

$\Rightarrow (127)^{1 / 3}=5+\frac{(2.6667)}{100}=5.02667 \cong 5.0267$