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UKMT Senior Mathematical Challenge, 2016

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

For which value of $k$ is $\sqrt{2016} + \sqrt{56}$ equal to $14^k$ ?

(A) $\frac{1}{2}$ (B) $\frac{3}{4}$ (C) $\frac{5}{4}$ (D) $\frac{3}{2}$ (E) $\frac{5}{2}$

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