Graduate Management Admission Test (GMAT) Practice Test

How can the square root of a number a be expressed in exponential form?

1. a

2. a^(1/2)

3. (√a)²

4. √(a²)

The correct answer is: a^(1/2)

The square root of a number \( a \) can be expressed in exponential form as \( a^{1/2} \). This notation arises from the properties of exponents, where taking the square root of a quantity is equivalent to raising that quantity to the power of one-half. In mathematical terms, if \( b = \sqrt{a} \), then by the definition of square roots, we can write \( b^2 = a \). Therefore, we can express \( b \) as \( a^{1/2} \), since squaring \( a^{1/2} \) leads back to \( a \). The other options do not accurately represent the expression of the square root in exponential form. For instance, expressing it as \( a \) is just the number itself, while \( (√a)² \) simplifies to \( a \), essentially returning to the original number. \( √(a²) \) also simplifies to \( a \) for non-negative values of \( a \), which does not reflect the exponential expression for the square root. Therefore, the choice that accurately represents the square root in exponential form is \( a^{1/2} \).