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

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

Latest revision as of 23:17, 27 April 2008

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