Answer:
Is irrational
Step-by-step explanation:
Let [tex]r[/tex] be a rational number, and [tex]i[/tex] be an irrational number. If their sum were rational, say [tex]q[/tex], then we'd have
[tex]r+i=q \iff i=q-r[/tex]
but [tex]q-r[/tex] is the difference between two rational numbers, and thus a rational number. But it also equals [tex]i[/tex], which is irrational by hypothesis. Since we have a contradiction, we conclude that the sum of a rational and an irrational can't be rational.
