# 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 only integers we get can from our expression are square roots less than 120. The highest is | + | 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 | 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)''' | And our answer is '''11, (E)''' | ||

+ | |||

== See Also == | == See Also == | ||

*[[2006 AMC 10A Problems]] | *[[2006 AMC 10A Problems]] |

## Revision as of 10:44, 2 August 2006

## Problem

For how many real values of is an integer?

## Solution

Since cannot be negative, the only integers we get can from our expression are square roots less than 120. The highest is

Thus our set of values is

And our answer is **11, (E)**