Certainly! Let's look at the equation [tex]\(\sqrt{2} \cdot 3 = 3 \cdot \sqrt{2}\)[/tex]. We need to determine which property of real numbers this equation illustrates.
First, we recognize that the equation involves two numbers, [tex]\(\sqrt{2}\)[/tex] and [tex]\(3\)[/tex], that are being multiplied together in two different orders. Specifically, they are arranged as:
[tex]\[ \sqrt{2} \cdot 3 \][/tex]
and
[tex]\[ 3 \cdot \sqrt{2} \][/tex]
Notice that the product remains the same regardless of the order in which the numbers are multiplied. This holds true for any real numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[ a \cdot b = b \cdot a \][/tex]
This characteristic of multiplication is defined by the Commutative Property of Multiplication. The commutative property states that the order in which two numbers are multiplied does not affect the product.
Therefore, the property illustrated by the equation [tex]\(\sqrt{2} \cdot 3 = 3 \cdot \sqrt{2}\)[/tex] is the:
[tex]\[ \boxed{\text{Commutative Property}} \][/tex]
