Question

\(\left(\sqrt{10}-\sqrt{2}\right)\cdot\sqrt{3+\sqrt{5}}\)

Answer 1

`( \sqrt{10} - \sqrt{2} ) . \sqrt{3 + \sqrt{5}}`

`= \sqrt{10} . \sqrt{3 + \sqrt{5}} - \sqrt{2} . \sqrt{ 3 + \sqrt{5}}`

`= \sqrt{ 3.10 + 10\sqrt{5}} - \sqrt{3 . 2 + 2\sqrt{5}}`

`= \sqrt{ 25 + 2 . 5 . \sqrt{5} + ( \sqrt{5})^2} - \sqrt{(\sqrt{5})^2 + 2 . \sqrt{5} . 1 + 1^2}`

`= \sqrt{ ( 5 + \sqrt{5})^2} - \sqrt{ ( \sqrt{5} + 1 )^2}`

`= | 5 + \sqrt{5} | - | \sqrt{5} + 1 |`

`= 5 + \sqrt{5} - sqrt{5} - 1 = 4`