Question

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

Answer 1

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

Answer 2

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.