To prove that the product of the two rational numbers \( \sqrt{36} \) and \( \frac{5}{3} \) is a rational number, we first calculate \( \sqrt{36} \), which equals 6. Since 6 is a rational number (it can be expressed as \( \frac{6}{1} \)), we can multiply it by \( \frac{5}{3} \):
\[ 6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10. \]
The product is 10, which is also a rational number because it can be expressed as \( \frac{10}{1} \). A product of two rational numbers is always rational, as both can be expressed as a fraction, making their product a fraction as well.