Graduate Management Admission Test (GMAT) Practice Test

Which property indicates that the product of the square roots is equal to the square root of the product?

1. Associative Property

2. Distributive Property

3. Square Root Property

4. Commutative Property

The correct answer is: Square Root Property

The property that states the product of the square roots is equal to the square root of the product is known as the Square Root Property. This property can be mathematically expressed as follows: for any non-negative numbers \(a\) and \(b\), the relationship \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\) holds true. This fundamental property of square roots allows for the simplification of expressions and is essential in various mathematical operations, especially in solving equations involving square roots. Understanding this property is crucial for correctly manipulating expressions and solving problems in algebra. It applies broadly in both academic contexts and real-world scenarios, where square roots often come into play. The other properties listed, such as associative, distributive, and commutative, relate to the arrangement and combination of numbers during operations but do not express the specific relationship between the square roots and their products.