2) And if so, then \(\displaystyle 1 + \sqrt{x} = \sqrt{1} + \sqrt{x} = \sqrt{1 + x}\) ?

3) If 1 and 2 is true, then:

\(\displaystyle (1 + \sqrt{x})^2 = (\sqrt{1 + x})^2\)

But if you actually square \(\displaystyle (1 + \sqrt{x})^2 \) and \(\displaystyle (\sqrt{1 + x})^2\), you'll find out that they are different:

\(\displaystyle (1 + \sqrt{x})^2 = (1 + \sqrt{x})(1 + \sqrt{x}) = 1 + 2\sqrt{x} + x\)

\(\displaystyle (\sqrt{1 + x})^2 = 1 + x\)

Why is that?