The sum of a rational number and an irrational number produces an irrational number.

True. By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats. If you add a non-repeating, non-terminating decimal to a terminating decimal, you still have a non-repeating, non-terminating decimal. If you add a non-repeating, non-terminating decimal to a repeating decimal, you will no longer have a repeating decimal, so the result is irrational.

True

Step-by-step explanation:

Example: sqrt (5) (which decimals continue forever) will mean that if you did 5+sqrt (5) it would still have those decimals.