Prove that the product of the two rational numbers Sqrt 36 and 5/3 is a rational number. Find the product and explain how you know it is a rational number, and explain your reasoning in 2 sentences

1 answer

The square root of 36 is 6, which is a rational number, and 5/3 is also a rational number. The product of two rational numbers (6 and 5/3) is 6 × (5/3) = 30/3 = 10, which is a rational number because it can be expressed as a fraction of integers (10/1).

A number is considered rational if it can be expressed as the ratio of two integers. Since both components of the product are rational, their product must also be rational.