Final answer:
The equation provided illustrates the concept closest to the Identity Property of multiplication, as it shows a quantity equal to itself. However, no specific property directly addresses an expression remaining unchanged when repeated.
Step-by-step explanation:
The equation "2 times the square root of 5 times 7" equals "2 times the square root of 5 times 7" demonstrates the Identity Property of multiplication. This property states that a number multiplied by one will yield the number itself, which reflects the equivalence shown in the equation. However, in this case, since the equation is essentially stating that a quantity is equal to itself, it serves as an example of the property that anything is equal to itself, which could be considered a characteristic of identity, but there's no specific 'identity property' that involves an expression remaining the same when stated twice.
Neither the Associative Property which refers to the grouping of numbers, the Commutative Property which refers to the order of numbers, nor the Distributive Property which combines addition and multiplication, are illustrated by this equation. The Identity Property in this context is slightly mislabeled, but closest in description, as the other options described different algebraic rules entirely.