The value of $\sqrt{9-2\sqrt{11-6\sqrt{2}}}$ is closest to:
Answer & explanation
Correct answer: option 3
( 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