Here is a simple explaination.

When you square it you have,

A circle!

Of radius 2.

But the original function,

Is a semi-circle because we only take the positive side of the circle (since square root only returns positive values).

Since the radius it 2 it starts at zero and goes all the way until 2.

The curve cannot be a function. Because for example, lie on this curve. Thus, for an absicca (x) values we have two ordinate (y) values which means it cannot be a function.Why is not a function and is?

The other curve only has one value.

Because when you have the only solution (real) for y is .

While in the first curve there are two solutions for y, (because it has even degree).