Question

Thực hiện phép tính:

D= \(\sqrt{9+6\sqrt{2}}\) - \(\sqrt{9-6\sqrt{2}}\) - \(\sqrt{21-12\sqrt{3}}\)

Answer 1

\(D=\sqrt{9+6\sqrt{2}}-\sqrt{9-6\sqrt{2}}-\sqrt{21-12\sqrt{3}}\)

\(D=\sqrt{9+2.\sqrt{3}.\sqrt{3}.\sqrt{2}}-\sqrt{9-2\sqrt{3}.\sqrt{3}.\sqrt{2}}-\sqrt{21-2.2\sqrt{3}.3}\)

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

\(-\sqrt{3^2-2.3.2\sqrt{3}+\left(2\sqrt{3}\right)^2}\)

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

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