Question

Which equations support the fact that rational numbers are closed under addition?

Select each correct answer.

9√+9√=29√9+9=29

13+13=2313+13=23

6√+(−6√)=06+(−6)=0

2√+2√=22√

Answer 1

Just took the test, the answer is;
`\sqrt 9 + \sqrt 9 = 2 \sqrt9              and (1)/(3) + (1)/(3) = (2)/(3)`

Answer 2

Answer:
`√(9) + √(9) = 2√(9)`

`(1)/(3) + (1)/(3) = (2)/(3)`

Explanation:

Since, according to the property that rational numbers are closed under addition.

If a and b are the rational number then (a+b) must be a rational number.

Since, In First option
`√(9) + √(9) = 2√(9)`

Addends √ 9 and √ 9 are rational number.

Also, 2 √9 is the rational number.

Thus It is following the property.

In Second option
`(1)/(3) + (1)/(3) = (2)/(3)`

Addends
`(1)/(3)` and
`(1)/(3)` are rational numbers.

Also,
`(2)/(3)` is a rational number.

Thus, It is also following the property.

Note: Both √6 and √2 are the irrational numbers.

This is why we did not take them.