Can I sum summands within square root?

Question

For example, here's an expression: $\sqrt{x^2 + x^2}$. Will it be equal to $\sqrt{2x^2}$?

Answer 1

Yes. $$\sqrt{x^2+x^2}\equiv \sqrt{2x^2}$$

However, be careful that $$\sqrt{x^2+\sqrt{x^2}}\neq\sqrt{2x^2}\neq\sqrt{x^2}+\sqrt{x^2}$$