Simplify. \( \sqrt{192}+5 \sqrt{243} \) \( [?] \sqrt{\square} \)

To simplify \( \sqrt{192}+5 \sqrt{243} \), first simplify each square root separately. For \( \sqrt{192} \): \[ 192 = 64 \times 3 = 8^2 \times 3. \] Therefore, \[ \sqrt{192} = \sqrt{64 \times 3} = \sqrt{64} \cdot \sqrt{3} = 8\sqrt{3}. \] For \( 5\sqrt{243} \): \[ 243 = 81 \times 3 = 9^2 \times 3. \] Thus, \[ \sqrt{243} = \sqrt{81 \times 3} = \sqrt{81} \cdot \sqrt{3} = 9\sqrt{3}. \] Multiplying by 5 gives \[ 5\sqrt{243} = 5 \cdot 9\sqrt{3} = 45\sqrt{3}. \] Now, combine the simplified parts: \[ \sqrt{192} + 5\sqrt{243} = 8\sqrt{3} + 45\sqrt{3} = (8 + 45)\sqrt{3} = 53\sqrt{3}. \] So, the final answer is \[ \sqrt{192} + 5\sqrt{243} = 53\sqrt{3}. \] Thus, in the required format: \( 53\sqrt{3} \)