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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?
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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>
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| − | == Solution ==
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| − | 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>
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| − | Thus our set of values is
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| − | <center><math> \{11^2, 10^2, 9^2,\ldots,2^2, 1^2, 0^2\} </math></center>
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| − | And our answer is '''11, (E)'''
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| − | == See Also ==
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| − | *[[2006 AMC 10A Problems]]
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| − | *[[2006 AMC 10A Problems/Problem 9|Previous Problem]]
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| − | *[[2006 AMC 10A Problems/Problem 11|Next Problem]]
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| − | [[Category:Introductory Algebra Problems]]
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