Question

if p and q are two distinct irrational numbers, then which of the following is always an irrational number?

Answer 1

Ans is fourth option

Answer 2

Answer:

(4) (p²q + qp) /pq is always irrational.

The sum of a rational and irrational number is always irrational.

Step-by-step explanation:

The options for the above question are:

(1) p/q (2) pq  (3) (p+q)² (4)(p²q+qp)/pq

Solution:

(1) The quotient of two irrational numbers can be either rational or irrational.

(2) Similarly, the product of two irrational numbers can also be either rational or irrational.

(3) The same is the case with square of sum of two irrational numbers. It can be either rational or irrational.

(4) Here we have (p²q + qp) /pq = pq (p+1 )/pq = p+1

The sum of a rational and irrational number is always irrational.

Hence (4) (p²q + qp) /pq is always irrational.