To prove that the product of the two rational numbers \(\sqrt{36}\) and \(\frac{5}{3}\) is a rational number, we first calculate the product:
\[ \sqrt{36} = 6 \quad \text{(since 6 × 6 = 36)} \] Then, we find the product:
\[ 6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10 \]
The result \(10\) is clearly a rational number, as it can be expressed as \(\frac{10}{1}\). Additionally, since both \(\sqrt{36}\) (which is 6) and \(\frac{5}{3}\) are rational numbers, their product is also rational since the product of any two rational numbers is always rational.