Question

An approximate value of $\sqrt[4]{18}$ is

• A. 2.0512
• B. 2.0425
• C. 2.0625
• D. 2.0834

Answer 1

Answer: (C)

Let $y=f(x)=x^{1/4}$ and $x=16$ and $\Delta x=2$
So, $\Delta y=\left(\frac{dy}{dx}\right)\Delta x$
$=\frac{1}{4}\left(x^{-3/4}\right)\Delta x$
at $x=16$ and $\Delta x=2$
$\Delta y=\frac{1}{4}\times \frac{1}{8}\times 2=\frac{1}{16}$
and $y=(16{)}^{1/4}=2$
So, $y+\Delta y=2+\frac{1}{16}=2.0625$