Question

Suppose a is an irrational number

and is a rational number. Can
their sum be rational? Explain your
answer.

Answer 1

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

Explanation:

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.

Example:

`3+√(5) = 3+2.236067977...=5.236067977....`