To simplify \(\sqrt{27a}\), we start by breaking down \(27\) into its prime factors:
\[ 27 = 3^3. \]
Thus, we can rewrite \(27a\) as follows:
\[ 27a = 3^3 a. \]
Now, we can express the square root as:
\[ \sqrt{27a} = \sqrt{3^3 \cdot a}. \]
Next, we can separate the square root using the property \(\sqrt{x \cdot y} = \sqrt{x} \cdot \sqrt{y}\):
\[ \sqrt{27a} = \sqrt{3^3} \cdot \sqrt{a}. \]
We know that \(\sqrt{3^3} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}\). Therefore, we can substitute this back into our expression:
\[ \sqrt{27a} = 3\sqrt{3} \cdot \sqrt{a}. \]
This simplifies further to:
\[ \sqrt{27a} = 3\sqrt{3a}. \]
Thus, the simplified form of \(\sqrt{27a}\) is:
\[ \boxed{3\sqrt{3a}}. \]
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