Question

Let a and b be rational numbers and c be an irrational number.

Select the appropriate choice show whether each value is always rational, never rational, or sometimes rational.
a + b is

a-b is

c² is

a/b is

(a)(b) is

ac is

Answer 1

Explanation:

a, b are rational numbers.

c is an irrational number.

irrational numbers are all the real numbers that are not rational numbers. like square roots of not-squared numbers (e.g. sqrt(2), sqrt(3), pi, ...).

a + b is always rational.

a - b is always rational.

c² is sometimes rational (e.g. (sqrt(2))² = 2, but pi² is still irrational).

a/b is always rational for b <> 0.

(a)(b) is always rational.

ac is never rational.