Thanks Radix and anon,
I like this question, it is a difference of 2 squares question. (Just like Radix said )
$$\\\sqrt{7-4\sqrt3}\times \sqrt{7+4\sqrt3}\\\\
=\sqrt{(7-4\sqrt3)(7+4\sqrt3)}\\\\
=\sqrt{(7)^2-(4\sqrt3)^2}\\\\
=\sqrt{49-16\times 3}\\\\
=\sqrt{49-48}\\\\
=\sqrt{1}\\\\
=1$$
.