$\sqrt{784 x^{6} \mathrm{~m} 12}$

Step 1 ：\sqrt{784 x^{6} \mathrm{~m} 12}

Step 2 ：=\sqrt{2^4 \cdot 7^2 \cdot x^6 \cdot \mathrm{m} \cdot 2^2 \cdot 3^1}

Step 3 ：=\sqrt{(2^4 \cdot 2^2)(7^2)(x^6)(\mathrm{m})(3^1)}

Step 4 ：=\sqrt{(2^6)(7^2)(x^6)(\mathrm{m})(3^1)}

Step 5 ：=\sqrt{2^6} \times \sqrt{7^2} \times \sqrt{x^6} \times \sqrt{\mathrm{m}} \times \sqrt{3^1}

Step 6 ：=(2^3)(7)(x^3)\sqrt{\mathrm{m}3} = \boxed{56x^3\sqrt{3\mathrm{m}}}