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 $5.0267$

$(127{)}^{1/3}=(125+2{)}^{1/3}$
Let $y=f\left(x\right)=x^{1/3}$
$y+\Delta y=(x+\Delta x{)}^{1/3}$
$\Rightarrow \Delta y=(x+\Delta x{)}^{1/3}-x^{1/3}$
Also, $\Delta y=f^{\prime }\left(x\right)\Delta x$
$\Rightarrow (x+\Delta x{)}^{1/3}-x^{1/3}=\frac{1}{3}{x}^{-2/3}\Delta x$
Put $x=125,\Delta x=2$
$\Rightarrow (127{)}^{1/3}-5=\frac{1}{3}(5{)}^{-2}\left(2\right)$
$\Rightarrow (127{)}^{1/3}=5+0.0267=5.0267$