multiplication of rational and irrational number
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If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation, however, of a rational times an irrational will be irrational. A better statement would be: "The product of a non-zero rational number and an irrational number is irrational."
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multiplication of rational and irrational number is always irrational number
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