Graduate Management Admission Test (GMAT) Practice Test

What is the result of squaring the square root of a number a?

1. √a

2. a

3. 1

4. 0

The correct answer is: a

When you square the square root of a number \( a \), you are essentially performing two operations that are inverses of each other. The square root of \( a \), denoted as \( \sqrt{a} \), represents the value that, when multiplied by itself, gives you \( a \). Therefore, if you take that square root \( \sqrt{a} \) and square it, you are effectively reversing the square root operation. Mathematically, this can be expressed as: \[ (\sqrt{a})^2 = a \] This shows that when you square the square root of \( a \), you arrive back at the original number \( a \). This understanding reinforces the importance of recognizing how operations like squaring and square roots interact with one another. The result is independent of what \( a \) actually is, as long as \( a \) is a non-negative number (the square root is typically defined in this way in real number contexts). Hence, the correct result of squaring the square root of a number \( a \) is indeed \( a \).