Rút gọn: căn bậc hai (7 + 4 căn bậc hai 3) + căn bậc hai (7 -4 căn bậc hai 3)

\(\sqrt {7 + 4\sqrt 3 } + \sqrt {7 - 4\sqrt 3 } \)

\( = \sqrt {4 + 3 + 4\sqrt 3 } + \sqrt {4 + 3 - 4\sqrt 3 } \)

\( = \sqrt {{2^2} + 2.2\sqrt 3 + {{\left( {\sqrt 3 } \right)}^2}} + \sqrt {{2^2} - 2.2\sqrt 3 + {{\left( {\sqrt 3 } \right)}^2}} \)

\( = \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} \)

\( = 2 + \sqrt 3 + 2 - \sqrt 3 = 4\).