Hi. I am solving an exercise that's telling me to estimate the value of $\sqrt{4.1}\cdot \sin\left ( 0.8 \right )$ using the partial derivatives of $f\left ( x,y \right )=\sqrt{x}\sin y$, but I'm unsure what value to use as an approximation for $y$, or rather what value the exercise expects me to use.
Choosing $y=\frac{\pi }{4}$ gives a very good estimate, but the result (assuming my solution is correct) contains both $\pi$ and $\sqrt{2}$, both of which are irrational. Choosing $y=1$ instead yields a rational number, but the error is substantial (almost 40% of the true value).