Graduate Management Admission Test (GMAT) Practice Test

What is a perfect square?

1. An integer that cannot be divided

2. An integer which is the square of an integer

3. A rational number squared

4. A positive integer only

The correct answer is: An integer which is the square of an integer

A perfect square is defined as an integer that can be expressed as the square of another integer. In other words, if there is an integer \( n \) such that \( n^2 \) equals the number in question, that number is a perfect square. For example, the numbers 0, 1, 4, 9, 16, etc., are all perfect squares because they can be represented as \( 0^2, 1^2, 2^2, 3^2, 4^2 \), respectively. The concept of a perfect square is foundational in understanding number properties and is used in various areas, including algebra, geometry, and number theory. Identifying integers that are perfect squares can also assist in factoring and simplifying expressions. The options that could lead to misunderstanding include the requirement for an integer to be unable to be divided, which misrepresents the properties of integers, and the limitation of perfect squares to only positive integers. In fact, negative integers can also fall into certain mathematical contexts, such as in complex numbers, although traditionally perfect squares are considered among non-negative integers.