Question

State whether the given statement is true or false:

The product of a rational and an irrational is irrational

Answer 1

This statement is false.

Explanation:

If the rational number is 0, then (0 \times) (irrational) (= 0), which is rational. So the product of a rational and an irrational is not always irrational. It is irrational when the rational number is nonzero.