Question

Let a be a rational number and b be an irrational number. Is ab necessarily an irrational number? Justify your answer with an example.

Answer 1

Hi there !!
Answer down here ⬇️⬇️

Given that ,
a is a rational number
and
b is an irrational Number

In most of the cases ,
ab will be irrational since product of a rational and an irrational number is 'generally' irrational.

But ,
if a = 0 [ 0 is a rational Number since 0=0/1]
and
b is an irrational number
than,
ab = 0 [ multiplication of any real number with 0 results in 0 ]

Here,
0 is a rational Number since it can be expected in p/q form as 0/1 where 0 and 1 are intergers and 1 is not equal to zero.

-----------------------

Hope it helps :D