Question

What is the square root of -10 degrees C

Answer 1

It is an indication that a mistake has been made, or that your imagination is working well.

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There are no physical units that correspond to the square root of a degree C. Degrees C is an arbitrary scale, so the square root of a number from that scale has no meaning. In the world of complex numbers, the square root of a negative number is imaginary. By attaching units of degrees C to the number, you have escaped the world of complex numbers and made your way to fantasy land.

In short, it is anything you want it to call it, as it is not anything that is defined in the realm of math or physics in the world we usually deal with.