To simplify the expression $ \sqrt{9 + \sqrt{3}} $, we start by examining possible simplifications.

### Step 1: Assume a Simplified Form
Let's assume that the expression simplifies to a form like:

\[
\sqrt{9 + \sqrt{3}} = \sqrt{a} + \sqrt{b}
\]

where $ a $ and $ b $ are positive real numbers.

### Step 2: Square Both Sides
Square both sides to eliminate the square roots:

\[
9 + \sqrt{3} = (\sqrt{a} + \sqrt{b})^2
\]

Expanding

Discover how to simplify the expression $\sqrt{9 + \sqrt{3}}$ using a detailed step-by-step guide. This problem involves square roots and algebraic simplification techniques. Suitable for advanced high school students and beyond.

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