Question

Rút gọn

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

Answer 1

\(=\sqrt{15-2.3.\sqrt{6}}+\sqrt{33-2.2\sqrt{6}.3}=\sqrt{9-2.3.\sqrt{6}+6}+\sqrt{\left(2\sqrt{6}\right)^2-2.2\sqrt{6}.3+9}=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(2\sqrt{6}-3\right)^2}=I3-\sqrt{6}I+I2\sqrt{6}-3I=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

Answer 2

Lời giải:

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}=\sqrt{3^2-2.3\sqrt{6}+6}+\sqrt{24+9-2.\sqrt{24.9}}\)

\(=\sqrt{(3-\sqrt{6})^2}+\sqrt{(\sqrt{24}-\sqrt{9})^2}=|3-\sqrt{6}|+|\sqrt{24}-\sqrt{9}|\)

\(=3-\sqrt{6}+\sqrt{24}-\sqrt{9}=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)