Question

Identify the commutative property of addition from the given options:

• A. $(\sqrt{2}+\sqrt{3})+\sqrt{5}=\sqrt{2}+(\sqrt{3}+\sqrt{5})$
• B. $\sqrt{2}\times \frac{1}{\sqrt{2}}=1$
• C. $\sqrt{2}(\sqrt{3}+\sqrt{5})=(\sqrt{2}\times \sqrt{3})+(\sqrt{2}\times \sqrt{5})$
• D. $\sqrt{2}+\sqrt{3}=\sqrt{3}+\sqrt{2}$

Answer 1

The correct option is D $\sqrt{2}+\sqrt{3}=\sqrt{3}+\sqrt{2}$

An operation is commutative if changing the order of the operands does not change the result.
The commutative property of addition states the order in which the numbers are added does not matter.
a + b = b + a.

• a ( b + c) = (a x b) + (a x c) represents the Distributive Property.
• (a+b)+c = a+(b+c) represents the Associative Property
• $a\times \frac{1}{a}=1$ represents multiplicative inverse.

Hence, $\sqrt{2}+\sqrt{3}=\sqrt{3}+\sqrt{2}$ illustrates commutative property of addition of irrational numbers.