\((a+b)^2=a^2+2\cdot a\cdot b+b^2\\ \\4+2 \sqrt{3}=1^2+2\cdot1\cdot \sqrt{3}+ \sqrt{3} ^2\ \ \ \Rightarrow\ \ \ a=1\ \ \ \wedge\ \ \ b= \sqrt{3} \\ \\4+2 \sqrt{3} =(1+ \sqrt{3} )^2\\ \\ \sqrt{4+2 \sqrt{3}} = \sqrt{(1+ \sqrt{3} )^2} =|1+ \sqrt{3} |=1+ \sqrt{3}\)
