Question

Square root of 4+2 root 3

Answer 1

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

Answer 2

`(a+b)^2=a^2+2ab+b^2\ \ \ (*)\\\\\\√(4+2\sqrt3)=√(3+2\sqrt3+1)=\sqrt{\underbrace{(\sqrt3)^2+2\cdot\sqrt3\cdot1+1^2}_((*))}\\\\=√((\sqrt3+1)^2)=|\sqrt3+1|=\sqrt3+1`