Question

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

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Hope it helps :D

Answer 2

Answer:

yes ab is necessarily irrational number because

Step-by-step explanation:

If ab is a rational number than

ab = p/q (where p and q are prime numbers)

b = p/q/a

b = p/qa

Now,p/qa is a rational number so obviously b will be rational but it is given that b is irrational so p/qa us irrational.

Hence, ab is irrational number.