Open a mathematics textbook printed in 1950 and you will not find a single answer with a square root underneath a line. There is a reason, and it has nothing to do with beauty.
Before calculators, every division was done by hand. Suppose you needed one divided by the square root of two. You would look up the square root of two in a table — 1.41421 — and then face the job of dividing 1 by 1.41421, which is a long division with a five-figure divisor and plenty of room for a mistake.
Now move the root upstairs. The same quantity can be written as the square root of two divided by two, and that is 1.41421 halved: 0.70711. A schoolchild can do it in five seconds and get it right.
The two expressions are the same number, written differently — but one of them took a minute of careful work and the other took a breath. Multiplied across a page of calculations, that difference decided how long a engineer worked and how often he was wrong.
So the habit spread, and it stayed after the reason for it disappeared. Today it is a convention, not a rule of arithmetic: examiners still write answers with the radical on top, so a pupil who leaves it underneath may have the right value and still fail to find it among the choices.
Which is a small lesson about mathematics in general. Some of what looks like law is only habit — but habits are worth knowing, because the answer sheet was written by somebody who has them.