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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√

Verified Answer :

Bordeom

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

Answer: \(\sqrt{9} + \sqrt{9} = 2\sqrt{9}\)

\(\frac{1}{3} + \frac{1}{3} = \frac{2}{3}\)

Step-by-step 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 \(\sqrt{9} + \sqrt{9} = 2\sqrt{9}\)

Addends √ 9 and √ 9 are rational number.

Also, 2 √9 is the rational number.

Thus It is following the property.

In Second option \(\frac{1}{3} + \frac{1}{3} = \frac{2}{3}\)

Addends \(\frac{1}{3}\) and \(\frac{1}{3}\) are rational numbers.

Also, \(\frac{2}{3}\) 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.

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