2021 AMC 12A Problem 2

Under what conditions is \sqrt{a^2+b^2}=a+b true, where a and b are real numbers?

\textbf{(A) } It is never true.

\textbf{(B) } It is true if and only if ab=0.

\textbf{(C) } It is true if and only if a+b\ge 0.

\textbf{(D) } It is true if and only if ab=0 and a+b\ge 0.

\textbf{(E) } It is always true.

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.