tính `\sqrt{4+\sqrt{10+2\sqrt{5}}}+ \sqrt{4-\sqrt{10+2\sqrt{5}}}`

$\begin{array}{l} a = \sqrt {4 + \sqrt {10 + 2\sqrt 5 } }  + \sqrt {4 – \sqrt {10 + 2\sqrt 5 } } \\  \Rightarrow {a^2} = 4 + \sqrt {10 + 2\sqrt 5 }  + 4 – \sqrt {10 + 2\sqrt 5 }  + 2.\sqrt {\left( {4 + \sqrt {10 + 2\sqrt 5 } } \right)\left( {4 – \sqrt {10 + 2\sqrt 5 } } \right)} \\  \Rightarrow {a^2} = 8 + 2.\sqrt {16 – \left( {10 + 2\sqrt 5 } \right)} \\  \Rightarrow {a^2} = 8 + 2.\sqrt {6 – 2\sqrt 5 }  = 8 + 2.\sqrt {{{\left( {\sqrt 5  – 1} \right)}^2}}  = 8 + 2\sqrt 5  – 2 = 6 + 2\sqrt 5  = {\left( {\sqrt 5  + 1} \right)^2}\\  \Rightarrow a = \sqrt 5  + 1\left( {a > 0} \right) \end{array}$