Answers:
- Rational
- Rational
- Rational
- Irrational
- Rational
- Irrational
In short, 4 and 6 are irrational. Everything else is rational.
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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.
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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.
