Graduate Management Admission Test (GMAT) Practice Test

What happens to the square root of a proper fraction compared to the fraction itself?

1. It becomes smaller

2. It remains the same

3. It becomes larger

4. It becomes zero

The correct answer is: It becomes larger

The square root of a proper fraction is smaller than the fraction itself. A proper fraction is defined as any fraction where the numerator is less than the denominator, resulting in a value between 0 and 1. When you take the square root of a proper fraction, you are finding a number which, when multiplied by itself, gives you the original fraction. Since the original fraction is less than 1, its square root will also be less than the fraction itself. For example, consider the proper fraction 1/4. The square root of 1/4 is 1/2, which is greater than 1/4. Thus, the value of the square root is indeed larger than the proper fraction itself. This general behavior applies to any proper fraction. The correct answer reflects the relationship accurately, showing that the square root of a proper fraction is greater than the fraction itself, while other options do not hold true in this context.