Question

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

Select each correct answer.

A. √2+√2=2√2

B. √6+(-√6)=0

C. √9+√9=2√9

D. 1/3+1/3=2/3

Answer 1

Explanation:

None of the given equations support the fact that rational numbers are closed under addition, because they all involve irrational numbers or fractions, which are not necessarily rational.

Option (A) involves the irrational number √2.

Option (B) involves adding the irrational number √6 with its negative, which results in a rational number, but it doesn't prove that all additions of rational numbers are also rational.

Option (C) involves the perfect square 9, but the square root of a non-square integer is generally an irrational number.

Option (D) involves the addition of two rational numbers, which is a valid example of the closure property of rational numbers under addition.

Therefore, the correct answer is (D) 1/3+1/3=2/3.