Question

\(\sqrt{15-\sqrt{216}}\)

Answer 1

\(\sqrt{15-\sqrt{216}}=\sqrt{15-6\sqrt{6}}=\sqrt{9-2.3.\sqrt{6}+6}=\sqrt{\left(3-\sqrt{6}\right)^2}\)

\(=\left|3-\sqrt{6}\right|=3-\sqrt{6}\)

Answer 2

\(\sqrt{15-\sqrt{216}}\)=\(\sqrt{15-6\sqrt{6}}\)=\(\sqrt{9+6-2×3\sqrt{6}}\)=\(\sqrt{9-\sqrt{6}}\) =\(\sqrt{(3-\sqrt{6})^2}\)=\(\left|3-\sqrt{6}\right|\)=\(3-\sqrt{6}\)