`\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}.\sqrt{4+\sqrt{32}}`

`=\sqrt{(2+\sqrt{2+\sqrt{2}})(2-\sqrt{2+\sqrt{2}})}.\sqrt{4+\sqrt{32}}`

`=\sqrt{2^2-(\sqrt{2+\sqrt{2}})^2}.\sqrt{4+\sqrt{32}}`

`=\sqrt{4-2-\sqrt{2}}.\sqrt{4+4\sqrt{2}}`

`=\sqrt{2-\sqrt{2}}.\sqrt{4+4\sqrt{2}}`

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

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

`=2\sqrt{\sqrt{2}}`