the product of a non zero rational no and an irrational number is?

Asked by  | 14th May, 2011, 12:00: AM

Expert Answer:

Product of non-zero rational number and an irrational number is always irrational.

Suppose a is rational (and non-zero) and x is irrational. Suppose ax is rational;
write ax = b where b is rational.

Then x = b/a, and x would be rational, contradiction. Hence the product is always irrational.

Answered by  | 14th May, 2011, 11:59: AM

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