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Square root is an integer

Source: AMC 12 2006A, Problem 10

February 5, 2006
AMC

Problem Statement

For how many real values of x x is \sqrt {120 \minus{} \sqrt {x}} an integer? <spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>9<spanclass=′latex−bold′>(D)</span>10<spanclass=′latex−bold′>(E)</span>11 <span class='latex-bold'>(A) </span> 3\qquad <span class='latex-bold'>(B) </span> 6\qquad <span class='latex-bold'>(C) </span> 9\qquad <span class='latex-bold'>(D) </span> 10\qquad <span class='latex-bold'>(E) </span> 11
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