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The product of a non-zero number and an irrational number is:
- a)always irrational
- b)always rational
- c)rational or irrational
- d)one
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The product of a non-zero number and an irrational number is:a)always ...
Product of a non-zero rational and an irrational number is always irrational.
i.e., 
Most Upvoted Answer
The product of a non-zero number and an irrational number is:a)always ...
Irrational as as any number multiplied to an irrational number results as irrational number.
eg. 2√3
here 2 is non zero number
but √3 is irrational
the product is 2√3 which is irrational
proof:
let 2√3 is rational number which can be written in the form
2√3=p/q---1(p and q are co prime integers and q≠0)
dividing by 2 both side in 1
√3=p/2q
here p/2q is rational but √3 is irrational hence it contradicts our assumption that the assumed number is rational
hence it is irrational
eg. 2√3
here 2 is non zero number
but √3 is irrational
the product is 2√3 which is irrational
proof:
let 2√3 is rational number which can be written in the form
2√3=p/q---1(p and q are co prime integers and q≠0)
dividing by 2 both side in 1
√3=p/2q
here p/2q is rational but √3 is irrational hence it contradicts our assumption that the assumed number is rational
hence it is irrational
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