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

To find the product of the two rational numbers \( \sqrt{36} \) and \( 53 \), we first calculate \( \sqrt{36} \), which is \( 6 \) (since \( 6 \times 6 = 36 \)).

Now, we calculate the product:

\[ 6 \times 53 = 318 \]

Since both \( 6 \) and \( 53 \) are rational numbers (as integers are a subset of rational numbers), their product, \( 318 \), is also a rational number.

Rational numbers are defined as numbers that can be expressed as the quotient of two integers (where the denominator is not zero); since \( 318 \) can be expressed as \( \frac{318}{1} \), it confirms that the product is rational.