$\sqrt{ \left( 2+\sqrt{ 3 } \right) \times \left( 2+\sqrt{ 2+\sqrt{ 3 } } \right) \times \left( 2-\sqrt{ 2+\sqrt{ 3 } } \right) }$
Use $\left( a-b \right)\left( a+b \right)={a}^{2}-{b}^{2}$ to simplify the product$\sqrt{ \left( 2+\sqrt{ 3 } \right) \times \left( 4-\left( 2+\sqrt{ 3 } \right) \right) }$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$\sqrt{ \left( 2+\sqrt{ 3 } \right) \times \left( 4-2-\sqrt{ 3 } \right) }$
Subtract the numbers$\sqrt{ \left( 2+\sqrt{ 3 } \right) \times \left( 2-\sqrt{ 3 } \right) }$
Use $\left( a-b \right)\left( a+b \right)={a}^{2}-{b}^{2}$ to simplify the product$\sqrt{ 4-3 }$
Subtract the numbers$\sqrt{ 1 }$
Any root of $1$ equals $1$$1$