Graduate Management Admission Test (GMAT) Practice Test

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Which expression is NOT equivalent to the square root of the difference between two numbers a and b?

(√a) - (√b)
√(a - b)
√a - √b
√(ab)

The correct answer is: √(a - b)

The square root of the difference between two numbers, denoted as √(a - b), represents the square root of the value obtained when the smaller number, b, is subtracted from the larger number, a. To determine which expression is not equivalent to this, it's essential to consider the properties of square roots and differences. The square root function does not distribute over subtraction. Therefore, the expression (√a) - (√b) and its equivalent formulation, √a - √b, suggest that both represent the individual square roots of a and b subtracted from each other, not the square root of their difference. Additionally, √(ab) represents the square root of the product of a and b, which also does not correspond to the square root of the difference between the two numbers. Focusing on option B, √(a - b) is precisely the expression given in the question. It is not just another representation but is, in fact, equal to itself. Thus, it is not equivalent to any of the other expressions provided, particularly those that manipulate the square roots individually rather than the difference of a and b as a singular entity. In summary, since √(a - b) represents the square