The value of $\sqrt{6 - \sqrt{17 - 2\sqrt{72}}}$ is closest to:
Answer & explanation
Correct answer: option 1
( a - b )2 = a2 + b2 - 2ab
$\sqrt{6 - \sqrt{17 - 2\sqrt{72}}}$
= $\sqrt{6 - \sqrt{(\sqrt{9} - \sqrt{8})^2}}$
= $\sqrt{6 - \sqrt{(3 - \sqrt{8})^2}}$
= $\sqrt{6 - 3 + \sqrt{8}}$
= $\sqrt{3 + 2.82}$
= 2.4