To determine the type of number that results from \( 512 \cdot \sqrt{16} \), let’s break it down:
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Evaluate \(\sqrt{16}\): \(\sqrt{16} = 4\), since \(4 \times 4 = 16\).
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Now, calculate \(512 \cdot 4\): \(512 \cdot 4 = 2048\).
Next, let's evaluate the options given:
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Radical, because one factor is a radical. - Incorrect, since \(\sqrt{16}\) simplifies to a rational number (4).
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Irrational, because both factors are irrational. - Incorrect, since \(512\) (which is a whole number) and \(\sqrt{16}\) (which simplifies to 4) are both rational numbers.
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Rational, because both numbers are rational. - Correct, \(512\) is rational and \(4\) is rational, and the product \(2048\) is also rational.
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Irrational, because one factor is irrational. - Incorrect, as explained above.
Therefore, the correct response is:
Rational, because both numbers are rational.