Difference between revisions of "2002 AMC 10P Problems/Problem 1"
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Revision as of 15:59, 14 July 2024
Problem
Which of the following numbers is a perfect square?
Solution 1
For a positive integer to be a perfect square, all the primes in its prime factorization must have an even exponent. With a quick glance at the answer choices, we can eliminate options
because 
is an odd power
because 
and 
is an odd power
because and is an odd power, and
because is an odd power.
This leaves option 
in which 
, and since 
and 
are all even, 
is a perfect square. Thus, our answer is 
.
See also
| 2002 AMC 10P (Problems • Answer Key • Resources) | ||
| Preceded by 2001 AMC 10 Problems |
Followed by 2002 AMC 10A Problems | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
