To prove that the product of the two rational numbers \(\sqrt{36}\) and \(53\) is a rational number, we first simplify \(\sqrt{36}\), which is equal to \(6\). Next, we compute the product:
\[ 6 \times 53 = 318. \]
Since both \(6\) and \(53\) are rational numbers (as they can be expressed as the fraction \(\frac{6}{1}\) and \(\frac{53}{1}\), respectively), and the product of any two rational numbers is also a rational number, we know that \(318\) is rational. Thus, the product \(\sqrt{36} \times 53\) is rational because it simplifies to \(318\).
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