Question

\(\sqrt{12-3\sqrt{15}}\)

Answer 1

\(\sqrt{12-3\sqrt{15}}=\sqrt{\left(\sqrt{\dfrac{15}{2}}-\sqrt{\dfrac{9}{2}}\right)^2}=\sqrt{\dfrac{15}{2}}-\sqrt{\dfrac{9}{2}}=\dfrac{\sqrt{30}}{2}-\dfrac{3\sqrt{2}}{2}\)

Answer 2

\(\sqrt{12-3\sqrt{15}}\)

\(=\dfrac{\sqrt{24-6\sqrt{15}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{15}-3}{\sqrt{2}}=\dfrac{\sqrt{30}-3\sqrt{2}}{2}\)