2006 AMC 12A Problems/Problem 10
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- The following problem is from both the 2006 AMC 12A #10 and 2006 AMC 10A #10, so both problems redirect to this page.
Problem
For how many real values of 
is 
an integer?
Solution
For to be an integer, 
must be a perfect square.
Since 
can't be negative, 
.
The perfect squares that are less than or equal to 
are 
, so there are 
values for .
Since every value of gives one and only one possible value for , the number of values of is 
.
See also
| 2006 AMC 12A (Problems • Resources) | ||
| Preceded by Problem 9 | Followed by Problem 11 | |
| 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 | ||
| 2006 AMC 10A (Problems • Resources) | ||
| Preceded by Problem 9 | Followed by Problem 11 | |
| 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 | ||
