Suppose that we have a line segment of length $8.4$ units. Is it possible to draw another line segment of length $8.4^2$ units, using only an unmarked straight edge and compass? I have no clue about how to approach this problem.
I could think of only one solution, first draw of square of side length $8.4$ units. Then squish the square, keeping its area constant, till one of its sides become unity, and hence the other side of the rectangle thus formed measures $8.4^2$ units. But the actions of the process cannot be performed under the given contraints.
In principle all rational numbers are constructible.
You are given a length of $8.4$ and you're asked to multiply it by $8.4$. That's equivalent to multiplying it by $42$ then dividing it by $5$.
I'm sure you know how to multiply a line segment by extension and taking equal arcs on your compasses.
For the division, follow a method similar to this: https://youtu.be/CLMu6Wadux0
Just in case you're limited in the space (paper or screen) you can work with, you can also multiply the original segment by $8$, mark that off, then extend it by twice the original, then divide into fifths as before. That's basically $8 + \frac 25 = 8.4$ times the original.
Also, just for completeness, I will state that the point raised by Theophile is a valid one - you cannot square an arbitrary unknown length unless you are also provided another line segment of defined length (say $1$ unit). In your specific problem, that is not an issue as you are told that your original segment is $8.4$ units long.