Question

Let x be rational and y be irrational. xy is always irrational. TRUE False​

Answer 1

Since quotient of two non-zero rational number is a rational number.So xy/x is a rational number => y is a rational number. But this contradicts the fact that y is an irrational number. Thus our supposition is wrong. Hence xy is an irrational number.

Answer

Let x=0 (a rational number) and y=  

3

​

 be an irrational number. Then,

xy=0(  

3

​

)=0, which is not an irrational number.

Hence, xy is not necessarily an irrational number.

Answer 2

Answer:

Here is your answer

Step-by-step explanation:

If a rational and an irrational is multiplied, added, subtracted or divided then their answer will be irrational.

So product of rational and irrational is always irrational.