A problem

Algebra Level 3

If \(a+b+c =6,\) where \(a, b\) and \(c\) are real numbers greater than or equal to \(- \frac{1}{4},\) what is the range of the following expression:

\[ \sqrt{4a +1} + \sqrt{4b +1} + \sqrt{4c+1}? \]

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