Search any question & find its solution
Question:
Answered & Verified by Expert
An approximate value of $\sqrt[4]{18}$ is
Options:
Solution:
2922 Upvotes
Verified Answer
The correct answer is:
2.0625
Let $y=f(x)=x^{1 / 4}$ and $x=16$ and $\Delta x=2$
So, $\Delta y=\left(\frac{d y}{d x}\right) \Delta x=\frac{1}{4}\left(x^{-3 / 4}\right) \Delta x$
at $\quad x=16$ and $\Delta x=2$
$$
\Delta y=\frac{1}{4} \times \frac{1}{8} \times 2=\frac{1}{16} \text { and } y=(16)^{1 / 4}=2
$$
So, $\quad y+\Delta y=2+\frac{1}{16}=2.0625$
So, $\Delta y=\left(\frac{d y}{d x}\right) \Delta x=\frac{1}{4}\left(x^{-3 / 4}\right) \Delta x$
at $\quad x=16$ and $\Delta x=2$
$$
\Delta y=\frac{1}{4} \times \frac{1}{8} \times 2=\frac{1}{16} \text { and } y=(16)^{1 / 4}=2
$$
So, $\quad y+\Delta y=2+\frac{1}{16}=2.0625$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.