Sat May 14, 2011 By:

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

Expert Reply
Sat May 14, 2011

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.
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