Choose all of the sums that are RATIONAL.

Answers:

In short, 4 and 6 are irrational. Everything else is rational.

Explanation:

A rational number is one in the form p/q where p,q are integers and q is nonzero. In the case of something like 3/5, we have p = 3 and q = 5.

Any terminating decimal can be converted to a rational number. Eg: 0.125 = 125/1000.

Any whole number is a rational number. Eg: 5 = 5/1.

Adding any two rational numbers leads to some other rational number.

Based on what is mentioned above so far, this means choices 1 through 3 are rational sums.

Choice 4 is not rational because sqrt(2) is irrational. The rule is

irrational+rational = irrational

Choice 5 is a rational sum because sqrt(4) = 2 = 2/1

Choice 6 is irrational for similar reasons as choice 4. Here pi = 3.14... is irrational.