To evaluate \( 512 \cdot \sqrt{16} \):
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Calculate \( \sqrt{16} \): \[ \sqrt{16} = 4 \]
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Now substitute this back into the original expression: \[ 512 \cdot \sqrt{16} = 512 \cdot 4 \]
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Perform the multiplication: \[ 512 \cdot 4 = 2048 \]
The result, \( 2048 \), is a rational number.
Therefore, the correct response is:
Rational because both factors are rational.