Q:

Why do we get the same result ,2-ball, for both sets, although they are not equal?

{${(x,y):x^2+y^2<1}$} and {$(x,y):\sqrt{x^2+y^2}<1$} $x,y\in\mathbb{R}$ These are the sets, but why do we get the same result why isnt the square root not changing the result ? 

A:

Using the square root, you should realise that the first set is the same as
$$\{(x,y):\sqrt{x^2+y^2}< \sqrt{1}\}$$
Now, what is $\sqrt{1}$?

