Question

\(\sqrt{3-\sqrt{5}}\)+\(\sqrt{3+\sqrt{5}}\)

Answer 1

`\sqrt(3-\sqrt5)+\sqrt(3+\sqrt5) `

`=\sqrt( (6-2\sqrt5)/2) + \sqrt((6+2\sqrt5)/2)`

`=\sqrt( ((\sqrt5)^2 -2.\sqrt5 .1+1^2)/2) + \sqrt(((\sqrt5)^2-2.\sqrt5 .1 +1^2)/2)`

`=\sqrt(((\sqrt5-1)^2)/2) +\sqrt(((\sqrt5+1)^2)/2)`

`= (\sqrt5-1)/2 + (\sqrt5+1)/2`

`=(2\sqrt5)/2=\sqrt5`