Answer
Let $a=0$ and $b=1$. Then $\sqrt {a+b}=\sqrt {0+1}=\sqrt 0+\sqrt 1$$=\sqrt a+\sqrt b$, because $\sqrt 0=0$ and $\sqrt 1=1$. Since $0$ and $1$ are real numbers, we conclude that there are real numbers $a$ and $b$ such that $\sqrt {a+b}=\sqrt a+\sqrt b$.
Work Step by Step
This proof is called a constructive proof of existence, whereby we prove that something exists by finding a specific example. For more on this method of proof, see the section entitled "Proving Existential Statements" beginning on page 148, especially example 4.1.3.
