Prove that the product of the two rational numbers √36 and 5/3 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

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:

1. Calculate \( \sqrt{36} \): \[ \sqrt{36} = 6 \]

2. Now multiply \( 6 \) by \( \frac{5}{3} \): \[ 6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10 \]

The result is \( 10 \), which is a rational number because it can be expressed as a fraction \( \frac{10}{1} \), where both the numerator and denominator are integers.

Thus, since the product of two rational numbers \( (6 \text{ and } \frac{5}{3}) \) yields another rational number, we conclude that the product is rational.