2006 AMC 10A Problems/Problem 10
Problem
For how many real values of is
an integer?
Solution
Since cannot be negative, the outermost radicand is at most 120. We are interested in the number of integer values that the expression can take, so we count the number of squares less than 120, the greatest of which is
Thus our set of values is
![$\{10^2, 9^2,\ldots,2^2, 1^2, 0^2\}$](http://latex.artofproblemsolving.com/e/d/8/ed8f03f4c1813dfbc0da06df0faf4f6d8efbfea7.png)
And our answer is 11, (E)