2006 CEMC Fermat Problems/Problem 4

Problem

The value $(\sqrt{\sqrt{9} + \sqrt{1}})^{4}$ is

$\text{ (A) }\ \sqrt{10} \qquad\text{ (B) }\ 10 \qquad\text{ (C) }\ 16 \qquad\text{ (D) }\ 82 \qquad\text{ (E) }\ 100$

$(\sqrt{\sqrt{9} + \sqrt{1}})^{4} = (\sqrt{3 + 1})^4 = (\sqrt{4})^4$

$=2^4 = \boxed {\textbf {(C) } 16}$

~anabel.disher

$(\sqrt{\sqrt{9} + \sqrt{1}})^{4} = (\sqrt{3 + 1})^{4 \times \frac{1}{2}}$

$=4^2 = \boxed {\textbf {(C) } 16}$

~anabel.disher