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Evaluate the given limit


    \[ \lim_{x \to 4} \sqrt{1+\sqrt{x}}. \]

Since we know x^r for r \in \mathbb{Q} is continuous and the composition of continuous functions is continuous, we know that the given function is continuous. Thus, the limit as x \to 4 is f(4),

    \[ \lim_{x \to 4} \sqrt{1 + \sqrt{x}} = \sqrt{1+\sqrt{4}} = \sqrt{3}. \]

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