1993 AHSME Problems/Problem 6

Problem

$\sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}}=$

$\text{(A) } \sqrt{2}\quad \text{(B) } 16\quad \text{(C) } 32\quad \text{(D) } (12)^{\tfrac{2}{3}}\quad \text{(E) } 512.5$

Solution

$\sqrt{\frac{ 8^{10}+4^{10} }{8^4 + 4^{11}}} = \sqrt{\frac{2^{30}+2^{20}}{2^{12}+2^{22}}}= \frac{ 2^{10} }{2^6} \sqrt{\frac{2^{10}+1}{1+2^{10}}} = 2^4$

$\fbox{B}$

1993 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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1993 AHSME Problems/Problem 6

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