Graduate Management Admission Test (GMAT) Practice Test

Which operation can be performed on the expression √(a²) assuming a is positive?

1. √a

2. ±a

3. a²

4. 0

The correct answer is: ±a

The expression √(a²) simplifies to a when assuming that a is positive. In mathematical terms, the square root of a squared value yields the original value if the original value is non-negative. Since a is positive, the square root operation produces a without ambiguity. The option that indicates ±a suggests that the square root of a number can be both positive and negative. This is generally true for square roots in broader terms because the equation x² = a can yield both positive and negative roots. However, in the context of the problem where a is specified as positive, the expression simplifies directly to a, making the use of ± here somewhat misleading in strict mathematical contexts. The other choices don't relate directly to the operation of taking the square root of a² efficiently: - Taking the square root of a (the first option) doesn't follow from the original expression. - a² represents squaring the value and isn’t the direct result of simplifying √(a²). - Zero does not pertain to the operation being performed on a² in this context. Thus, stating ±a accurately reflects the general behavior of square roots in mathematical expressions, even though it may not apply directly when we know the value is positive.