To simplify the expression \( \sqrt{81} \times \sqrt{16} \), we can first calculate each square root separately.
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Calculate \( \sqrt{81} \): \[ \sqrt{81} = 9 \]
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Calculate \( \sqrt{16} \): \[ \sqrt{16} = 4 \]
Now, we can multiply the results together: \[ \sqrt{81} \times \sqrt{16} = 9 \times 4 \]
Calculating the product: \[ 9 \times 4 = 36 \]
Now, we can express our answer in simplest radical form: Since \( 36 = \sqrt{36^2} = \sqrt{1296} \) but we are looking for it in the non-radical form, we actually conclude: \[ \sqrt{81} \times \sqrt{16} = 36 \]
Thus, the product in simplest radical form is: \[ \boxed{36} \]