Question

\(\sqrt{17-3\sqrt{32}}+\sqrt{17-3\sqrt{32}}\)

Answer 1

`\sqrt(17-3\sqrt32)+\sqrt(17+3\sqrt32)`

`=\sqrt(17-12\sqrt2)+\sqrt(17+12\sqrt2)`

`=\sqrt(9-12\sqrt2+8)+\sqrt(9+12\sqrt2+8)`

`=\sqrt(3^2-2.3.2\sqrt2 +(2\sqrt2)^2)+\sqrt(3^2+2.3.2\sqrt2+(2\sqrt2)^2)`

`=\sqrt((3-2\sqrt2)^2)+\sqrt((3+2\sqrt2)^2)`

`=3-2\sqrt2+3+2\sqrt2`

`=6`

Answer 2

\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)

\(=3-2\sqrt{2}+3+2\sqrt{2}\)

=6