To prove that the product of the two rational numbers \(\sqrt{36}\) and \(\frac{5}{3}\) is a rational number, we first evaluate \(\sqrt{36}\), which is \(6\) (since \(6 \times 6 = 36\)). Next, we multiply this result by \(\frac{5}{3}\):
\[ 6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10. \]
Since \(10\) can be expressed as the fraction \(\frac{10}{1}\), it is a rational number (as any integer can be expressed as a fraction where the denominator is not zero). Thus, the product is a rational number.
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