(VI) \( \sqrt{\sqrt{28+\sqrt{64}}+\sqrt{37+\sqrt{144}}+12} \)

To simplify \( \sqrt{\sqrt{28+\sqrt{64}}+\sqrt{37+\sqrt{144}}+12} \), let's break it down step by step. 1. Simplify \( \sqrt{64} \) which is \( 8 \): \[ \sqrt{28+\sqrt{64}} = \sqrt{28 + 8} = \sqrt{36} = 6. \] 2. Simplify \( \sqrt{144} \) which is \( 12 \): \[ \sqrt{37+\sqrt{144}} = \sqrt{37 + 12} = \sqrt{49} = 7. \] 3. Now, we can substitute these results back into the original expression: \[ \sqrt{\sqrt{28+\sqrt{64}}+\sqrt{37+\sqrt{144}}+12} = \sqrt{6 + 7 + 12}. \] 4. Combine the numbers inside the square root: \[ 6 + 7 + 12 = 25. \] 5. Finally, take the square root: \[ \sqrt{25} = 5. \] Thus, the simplified expression is: \[ \boxed{5}. \]