Question

\(\sqrt{\dfrac{7-3\sqrt{5}}{162}}\)

Answer 1

\(\sqrt{\dfrac{7-3\sqrt{5}}{162}}\)

\(=\dfrac{\sqrt{7-3\sqrt{5}}}{\sqrt{162}}\)

\(=\dfrac{\sqrt{2}\cdot\sqrt{7-3\sqrt{5}}}{9\sqrt{2}\cdot\sqrt{2}}\)

\(=\dfrac{\sqrt{14-6\sqrt{5}}}{9\cdot2}\)

\(=\dfrac{\sqrt{3^2-2\cdot3\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}}{18}\)

\(=\dfrac{\sqrt{\left(3-\sqrt{5}\right)^2}}{18}\)

\(=\dfrac{3-\sqrt{5}}{18}\)