Prove that the product of the two rational numbers 36−−√

Question

and 53
is a rational number. Find the product and explain how you know it is a rational number. Explain your reasoning in 1–2 sentences.(2 points)

Answer 1

The expression \( \sqrt{36} \) simplifies to \( 6 \), a rational number. The second rational number is \( \frac{5}{3} \).

Now, we can calculate the product: \[ 6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10. \]

The result \( 10 \) is also a rational number because it can be expressed as \( \frac{10}{1} \). Thus, the product of \( \sqrt{36} \) and \( \frac{5}{3} \) is rational because both factors are rational, and the product of two rational numbers is always rational.