Let x and y be rational numbers. Show that xy is a rational number.

Question

KnowledgeBoat · Accepted Answer

Let x = , n 0 and y = , q 0, where m, n, p and q are integers. [By definition of rationals] So, Using properties of integers, mp and nq are integers and since n, q are not equal to zero. ∴ nq 0. ∴ is a rational number. Hence, proved that xy is also a rational number.

Mathematics

Let x and y be rational numbers. Show that xy is a rational number.

Mathematics Proofs

Related Questions

Take two consecutive odd numbers. Find the sum of their squares, and then add 6 to the result. Prove that the new number is always divisible by 8.

If p ≥ 5 is a prime number, show that p² + 2 is divisible by 3.

If a and b are positive integers, then you know that a = bq + r, 0 ≤ r < b, where q is a whole number. Prove that HCF (a, b) = HCF (b, r).

Mathematics

Let x and y be rational numbers. Show that xy is a rational number.

Mathematics Proofs

Related Questions

Take two consecutive odd numbers. Find the sum of their squares, and then add 6 to the result. Prove that the new number is always divisible by 8.

If p ≥ 5 is a prime number, show that p2 + 2 is divisible by 3.

If a and b are positive integers, then you know that a = bq + r, 0 ≤ r < b, where q is a whole number. Prove that HCF (a, b) = HCF (b, r).

If p ≥ 5 is a prime number, show that p² + 2 is divisible by 3.