To simplify the expression \( 2 \sqrt{27} - \sqrt{3} \), we can start by simplifying \( \sqrt{27} \).
First, we can express \( 27 \) as \( 9 \times 3 \): \[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \cdot \sqrt{3} = 3 \sqrt{3} \]
Now we can substitute \( \sqrt{27} \) in the expression: \[ 2 \sqrt{27} = 2 \cdot 3 \sqrt{3} = 6 \sqrt{3} \]
Now, we can rewrite the entire expression: \[ 6 \sqrt{3} - \sqrt{3} \]
Since both terms have a common factor of \( \sqrt{3} \), we can combine them: \[ 6 \sqrt{3} - 1 \sqrt{3} = (6 - 1) \sqrt{3} = 5 \sqrt{3} \]
Thus, the simplified expression is: \[ \boxed{5 \sqrt{3}} \]
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