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

To simplify \( \sqrt{192} + 5 \sqrt{243} \), we first break them down. Starting with \( \sqrt{192} \): \[ 192 = 64 \times 3 = 8^2 \times 3 \] Thus, \[ \sqrt{192} = \sqrt{64 \times 3} = \sqrt{64} \sqrt{3} = 8\sqrt{3} \] Next, we simplify \( 5 \sqrt{243} \): \[ 243 = 81 \times 3 = 9^2 \times 3 \] So, \[ \sqrt{243} = \sqrt{81 \times 3} = \sqrt{81} \sqrt{3} = 9\sqrt{3} \] Then, multiplying by 5: \[ 5 \sqrt{243} = 5 \times 9\sqrt{3} = 45\sqrt{3} \] Now, we combine: \[ \sqrt{192} + 5 \sqrt{243} = 8\sqrt{3} + 45\sqrt{3} = (8 + 45)\sqrt{3} = 53\sqrt{3} \] Thus, the simplified form is \( 53\sqrt{3} \). The final output is \([?] \sqrt{\square} = 53\sqrt{3}\).