Question

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

Answer 1

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{9+6-2.3.\sqrt{6}}+\sqrt{9+24-2.3.2\sqrt{6}}\)

\(=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3-2\sqrt{6}\right)^2}\)

\(=3-\sqrt{6}-3+2\sqrt{6}=\sqrt{6}\)

Answer 2

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{15-2.3\sqrt{6}}+\sqrt{33-2.6\sqrt{6}}\)

\(=\sqrt{15-2\sqrt{54}}+\sqrt{33-2\sqrt{216}}\)

\(=\sqrt{9-2\sqrt{6}\sqrt{9}+6}+\sqrt{24-2\sqrt{24}\sqrt{9}+\sqrt{9}}\)

\(=3-\sqrt{6}+\sqrt{24}-3\)

\(=\sqrt{24}-\sqrt{6}\)

\(=\sqrt{6}\)