Cut the square cloth!

Question

I have a square cloth with side length $x$ cm, and I am going to cut it into at least $n$ squares with side length $1$ cm for my customer, and also you cannot cut the cloth to thinner pieces (reminded by @risky mysteries). I cannot glue any bits of cloth together. What is the minimum value of $x$?

Problem inspired from a math test problem in my school (about a month ago).

Thanks to @Jaap Scherphuis, I now know this is an unsolved problem. So of course I still haven't solved it. You can use a computer!

risky mysteries · Answer

Is the answer

Reason:

Kable · Answer

Because

Amit Huda · Answer

In both the square, area will be the same.
suppose big square has area, A = x*x
all small square total area will be A = n * 1 *1
so,
x*x = n * 1 * 1
x = √n, for all x>=n

user3294068 · Answer

Clearly, $x geq sqrt n$, otherwise your original square would have less area than the n smaller squares.

However, for $n=5$,

So, in conclusion,

Cut the square cloth!

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