Question

Prove the product of two rational numbers is rational __________.

Options:
A) Using prime factorization
B) By contradiction
C) Inductive reasoning
D) Deductive reasoning

Answer 1

To prove the product of two rational numbers is rational, we can use prime factorization.

Step-by-step explanation:

The answer to the question is option A) Using prime factorization. To prove that the product of two rational numbers is rational using prime factorization, we need to show that the result of multiplying two rational numbers can be expressed as a fraction. Let's consider two rational numbers, a/b and c/d, where a, b, c, and d are integers and b and d are not equal to zero. The product of these two rational numbers is (a/b) * (c/d) = (a * c) / (b * d), which can be expressed as a fraction with integers in the numerator and denominator. Therefore, the product of two rational numbers is rational.