The value of $\sqrt{9-2\sqrt{11-6\sqrt{2}}}$ is closest to:

2.7 2.9 2.4 2.1

2.4

( a - b )2 = a2 + b2 - 2ab  $\sqrt{9-2\sqrt{11-6\sqrt{2}}}$ = $\sqrt{9 - 2\sqrt{(\sqrt{9} - \sqrt{2})^2}}$ = $\sqrt{9 - 2\sqrt{(3 - \sqrt{2})^2}}$ = $\sqrt{9 - 6 + 2\sqrt{2}}$ = $\sqrt{3 + 2.82}$ = 2.4