FTCE General Knowledge Math Practice Test

What is an important characteristic of irrational square roots?

1. They are always whole numbers.

2. They can be evaluated to a fraction.

3. They do not have an exact number that they evenly multiply by.

4. They are always negative.

The correct answer is: They do not have an exact number that they evenly multiply by.

The characteristic that irrational square roots possess is that they do not have an exact number that they evenly multiply by to produce a perfect square. This means that the square root of certain numbers cannot be expressed as a simple fraction or a whole number. For example, the square root of 2 is an irrational number because it cannot be expressed as a fraction and has a non-repeating, non-terminating decimal representation. In contrast, whole numbers result from the square root of perfect squares (like 1, 4, or 9), and fractions provide exact evaluations of numbers. Irrational numbers are defined by their inability to be expressed neatly in these forms, which is a hallmark of their nature. The concept of irrational square roots fundamentally ties into the broader understanding of rational versus irrational numbers in mathematics.