Question 26

If $$A = \sqrt{281 + \sqrt{53 + \sqrt{112 + \sqrt{81}}}}$$, $$B = \sqrt{92 + \sqrt{55 + \sqrt{75 + \sqrt{36}}}}$$ then $$A - B$$ is

Correct Answer: 7

Solution

Working from the innermost radical of $$A$$, $$\sqrt{81} = 9$$, then $$\sqrt{112 + 9} = 11$$, then $$\sqrt{53 + 11} = 8$$ and finally $$A = \sqrt{281 + 8} = \sqrt{289} = 17$$. Similarly for $$B$$, $$\sqrt{36} = 6$$, $$\sqrt{75 + 6} = 9$$, $$\sqrt{55 + 9} = 8$$ and $$B = \sqrt{92 + 8} = 10$$. Hence $$A - B = 17 - 10 = 7$$.

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