\begin{align} &\sqrt{10+4\sqrt{(\sqrt{2})^2+1^2-2\sqrt{2}}}\\ &=\sqrt{10+4\sqrt{(\sqrt{2}-1)^2}}\\ &=\sqrt{6+4\sqrt{2}}\\ &=\sqrt{2^2 + (\sqrt{2})^2+2\cdot 2\cdot\sqrt{2}}\\ &=\sqrt{(2+\sqrt{2})^2}\\ &=\boxed{2+\sqrt{2}} \end{align}