Problem: What is the value of the expression 1684?\sqrt{16 \sqrt{8 \sqrt{4}}}?1684?
Answer Choices:
A. 444 B. 424 \sqrt{2}42 C. 888 D. 828 \sqrt{2}82 E. 161616
Solution:
Simplifying yields
1684=1616=64=8\sqrt{16 \sqrt{8 \sqrt{4}}}=\sqrt{16 \sqrt{16}}=\sqrt{64}=81684=1616=64=8
Answer: C\boxed{C}C.
The problems on this page are the property of the MAA's American Mathematics Competitions