$\sqrt{ {\left( 2+\sqrt{ 3 } \right)}^{2} }+\sqrt{ 7-4\sqrt{ 3 } }$
Use ${a}^{2}-2ab+{b}^{2}={\left( a-b \right)}^{2}$ to factor the expression$\sqrt{ {\left( 2+\sqrt{ 3 } \right)}^{2} }+\sqrt{ {\left( 2-\sqrt{ 3 } \right)}^{2} }$
Reduce the index of the radical and exponent with $2$$2+\sqrt{ 3 }+\sqrt{ {\left( 2-\sqrt{ 3 } \right)}^{2} }$
Reduce the index of the radical and exponent with $2$$2+\sqrt{ 3 }+2-\sqrt{ 3 }$
Since two opposites add up to $0$, remove them from the expression$2+2$
Add the numbers$4$