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

Question

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 \(\sqrt{36}\) and \(\frac{5}{3}\) is a rational number, we first calculate the product:

\[ \sqrt{36} = 6 \]

Now, we find the product:

\[ 6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10 \]

Since 10 is an integer, it is also a rational number (a rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero). Thus, the product of \(\sqrt{36}\) and \(\frac{5}{3}\) is rational.