Question

show that the product of a non zero rational number with an irrational number is always irrational

Answer 1

Let a non zero rational number be 2 and an irrational number be √3, according to condition:-
2×√3=2√2
=>2√3 is an irrational number..
=>The product of a non zero rational number with an irrational number is always irrational.
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Answer 2

Non zero rational numbers are 1,2,3,4,5......

Irrational numbers are √2,√3,√5,√6......

Product of non zero rational number with irrational number.

1×√2 = √2

2×√2 = 2√2

4×√3 = 4√3

All results are irrational numbers.

Therefore,the product of a non zero rational number with an irrational number is always irrational.

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