Question

Which of the following statements is false?

The sum of two rational numbers is always rational.

The sum of a rational number and an irrational number is always rational.

The product of a nonzero rational number and an irrational number is always irrational.

The product of two irrational numbers is either rational or irrational.

Answer 1

The second one is false.

Explanation:

The sum of a rational and an irrational is always irrational.

For example, take `sqrt2 +1`, we don't know what `sqrt2` is, so we can't know what `1` more than it is.

This rule applies to any and every irrational.