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.
To prove that the product of the two rational numbers is a rational number, we need to show that it can be expressed as a fraction in the form of p/q, where p and q are integers and q is not equal to zero. The product of 36√ and 5/3 is (36√)(5/3) = (180√)/3 = 60√ = (60√)/(1) which can be expressed as a fraction and therefore is a rational number.
