The expression \( \sqrt{125} \) can be simplified as follows:
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First, factor \( 125 \) into its prime factors: \[ 125 = 5^3 \]
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Next, express \( \sqrt{125} \): \[ \sqrt{125} = \sqrt{5^3} = \sqrt{5^2 \cdot 5} = \sqrt{5^2} \cdot \sqrt{5} \]
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Simplify \( \sqrt{5^2} \): \[ \sqrt{5^2} = 5 \]
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Therefore: \[ \sqrt{125} = 5 \cdot \sqrt{5} \]
The simplified form of \( \sqrt{125} \) is \( 5\sqrt{5} \).