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No.Suppose a and b are two rational numbers.
Then they can be written as follows: a = p/q, b = r/s where p, q, r and s are integers and q, s >0.
Then a*b = (p*r)/(q*s).
Using the properties of integers, p*r and q*s are integers and q*s is non-zero. So a*b can be expressed as a ratio of two integers and so the product is rational.
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