Difference between revisions of "2006 AMC 10A Problems/Problem 10"

Latest revision as of 23:17, 27 April 2008

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-== Problem ==
+#redirect [[2006 AMC 12A Problems/Problem 10]]
-For how many real values of <math>\displaystyle x</math> is <math>\sqrt{120-\sqrt{x}}</math> an integer?
-<math> \mathrm{(A) \ } 3\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 11 </math>
-== Solution ==
-Since <math>\sqrt{x}</math> cannot be negative, the only integers we get can from our expression are square roots less than 120. The highest is
-<math>11^2=121</math>
-Thus our set of values is
-{<math>11^2, 10^2, 9^2,....2^2, 1^2, 0^2</math>}
-And our answer is '''11, (E)'''
-== See Also ==
-*[[2006 AMC 10A Problems]]