Emily states that the product of a nonzero rational number and an irrational number is sometimes rational and
sometimes irrational.
Which statement correctly describes whether Emily is correct or incorrect?
O Emily is incorrect. The product of a nonzero rational number and an irrational number is always irrational.
O Emily is incorrect. The product of a nonzero rational number and an irrational number is always rational.
0
Emily is correct. The product of a nonzero rational number and an irrational number may be rational or
irrational.



Answer :

Final answer:

The product of a nonzero rational number and an irrational number can be rational or irrational.


Explanation:

Emily is correct. The product of a nonzero rational number and an irrational number may be rational or irrational. This can be illustrated with examples:

  1. If you multiply 2 (a rational number) by √2 (an irrational number), the result is 2√2, which is irrational.
  2. However, if you multiply 2/3 (a rational number) by √9 (an irrational number), the result is 2, which is rational.

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