Difference between revisions of "2006 AMC 10A Problems/Problem 10"
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<math> \mathrm{(A) \ } 3\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 11 </math> | <math> \mathrm{(A) \ } 3\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 11 </math> | ||
== Solution == | == Solution == | ||
| − | Since <math>\sqrt{x}</math> cannot be negative, the | + | Since <math>\sqrt{x}</math> 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 <math>10^2=100.</math> |
Thus our set of values is | Thus our set of values is | ||
| − | <center><math> \{ | + | <center><math> \{10^2, 9^2,\ldots,2^2, 1^2, 0^2\} </math></center> |
And our answer is '''11, (E)''' | And our answer is '''11, (E)''' | ||
Revision as of 01:36, 28 February 2007
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
And our answer is 11, (E)
