1. The problem is to simplify the expression $2\sqrt{616}$.\n\n2. Recall the property of square roots: $a\sqrt{b} = \sqrt{a^2 b}$. Here, $2\sqrt{616}$ can be rewritten as $\sqrt{2^2 \times 616} = \sqrt{4 \times 616}$.\n\n3. Calculate inside the square root: $4 \times 616 = 2464$. So, $2\sqrt{616} = \sqrt{2464}$.\n\n4. Next, simplify $\sqrt{616}$ by factoring 616 into its prime factors or perfect squares.\n\n5. Factor 616: $616 = 4 \times 154$ because $4$ is a perfect square.\n\n6. Use the property $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$:\n$$\sqrt{616} = \sqrt{4 \times 154} = \sqrt{4} \times \sqrt{154} = 2\sqrt{154}.$$\n\n7. Substitute back into the original expression:\n$$2\sqrt{616} = 2 \times 2\sqrt{154} = 4\sqrt{154}.$$\n\n8. Check if $\sqrt{154}$ can be simplified further. Factor 154:\n$$154 = 2 \times 7 \times 11,$$ none of which are perfect squares, so $\sqrt{154}$ is simplified.\n\nFinal answer: $$2\sqrt{616} = 4\sqrt{154}.$$