Question

\(1,\sqrt{4+2\sqrt{3}}+\sqrt{3} 2,\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)

Answer 1

1: \(=\sqrt{3}+1+\sqrt{3}=2\sqrt{3}+1\)

2: \(=3+\sqrt{2}-3+\sqrt{2}=2\sqrt{2}\)

Answer 2

`1)\sqrt{4+2\sqrt{3}}+\sqrt{3}`

`=\sqrt{(\sqrt{3}+1)^2}+\sqrt{3}`

`=|\sqrt{3}+1|+\sqrt{3}`

`=\sqrt{3}+1+\sqrt{3}=2\sqrt{3}+1`

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`2)\sqrt{11+6\sqrt{2}}-3+\sqrt{2}`

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

`=|3+\sqrt{2}|-3+\sqrt{2}`

`=3+\sqrt{2}-3+\sqrt{2}=2\sqrt{2}`