Question

Let x be rational and y be irrational. Is xy necessarily irrational. Justify your answer with example.

Answer 1

Answer:

No because x can be 0 and any number multiplied by 0 is 0..

So it can be said that multiplication if a rational and an irrational number can give any between a ration and an irrational number ..

Hope it helps .

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Answer 2

Answer:

   yes , xy is necessarily an irrational number ( x ≠ 0 )

Step-by-step explanation:

let x be a rational number and y be an irrational number.

then xy is an irrational number when (x ≠ 0).

for example ,

x = 2   and   y = $\sqrt{2}$

then xy = 2$\sqrt{2}$    is an irrational number.

when x = 0

then xy = 0  is rational

thus xy is an irrational number only when x ≠ 0

Hope it helps !