Graduate Management Admission Test (GMAT) Practice Test

Which expression represents the product of the square roots of two numbers a and b?

1. √(a + b)

2. (√a) + (√b)

3. (√a) x (√b)

4. √(a - b)

The correct answer is: (√a) x (√b)

The product of the square roots of two numbers, a and b, is mathematically represented as the square root of their product, which can be expressed as \( \sqrt{a} \times \sqrt{b} \). When multiplying the square roots, the expressions can be combined under a single square root, leading to the equation \( \sqrt{a \times b} \). By selecting the third option, you're correctly recognizing that multiplying the square roots of \( a \) and \( b \) is the same as directly multiplying the two variables under the square root. This is a fundamental property of square roots in algebra, specifically, that \( \sqrt{x} \times \sqrt{y} = \sqrt{xy} \). The other options do not accurately represent the product of the square roots. The first option introduces addition under a square root, which alters the operation fundamentally. The second option suggests adding the square roots instead of multiplying them, which is also not the correct action for finding the product. The last option involves a subtraction under a square root, which does not relate to the product of the square roots of two numbers. Thus, the choice that accurately expresses the product of the square roots is indeed the one that correctly