Classify ( 7 )·(3) as rational or irrational, and explain your reasoning. A) Suppose an irrational times a nonzero rational = rational, then irrational = rational rational . This means irrational = rational. Thus the irrational number 7 times the rational number 3 equals 3 7 , which is both rational and irrational. B) Suppose an irrational times a nonzero rational = rational, then irrational = rational rational . This means irrational = rational, which is a contradiction. Thus the irrational number 7 times the rational number 3 equals the rational number 3 7 . C) Suppose an irrational times a nonzero rational = rational, then irrational = rational rational . This means irrational = rational, which is a contradiction. Thus the irrational number 7 times the rational number 3 equals the irrational number 3 7 . D) Suppose an irrational times a nonzero rational = rational, then irrational = rational rational . This means irrational = rational, which is a contradiction. Thus the irrational number 7 times the rational number 3 equals 3 7 , which is neither rational nor irrational.
