Question

Answer 1

\(\sqrt{3+\sqrt{8}}=\sqrt{3+2\sqrt{2}}=\sqrt{\sqrt{2}^2+2.1.\sqrt{2}+1^2}=\sqrt{\left(\sqrt{2}+1\right)^2}=\sqrt{2}+1\)

Answer 2

`\sqrt{3 + \sqrt{8}}`

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

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

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

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