3. If the inequality $\sqrt{a}+\sqrt{b} \leqslant m \sqrt[4]{a^{2}+b^{2}}$ holds for all positive real numbers $a, b$, then the minimum value of $m$ is ( ).
(A) 2
(B) $\sqrt{2}$
(C) $2^{\frac{3}{4}}$
(D) 4
3.C.

Since $\sqrt{a}+\sqrt{b} \leqslant \sqrt{2(a+b)} \leqslant \sqrt{2 \sqrt{\frac{a^{2}+b^{2}}{2}}}$. The equality holds if and only if $a=b$.
Therefore, $m \geqslant 2^{\frac{3}{4}}$, which means the minimum value of $m$ is $2^{\frac{3}{4}}$.