Question

Why is it important that √2 cannot be written as a repeating decimal?

a) Because it is an irrational number
b) Because it is a prime number
c) Because it is a complex number
d) Because it is an imaginary number

Answer 1

The square root of 2 is an irrational number and so it cannot be written as a repeating decimal. This is important as it reflects the concept of irrational numbers within the real number system.

Step-by-step explanation:

The importance of √2 not being able to be written as a repeating decimal relates to the nature of irrational numbers. The square root of 2 (√2) is indeed an irrational number, which means it cannot be expressed as a simple fraction or as a repeating or terminating decimal.

This is significant because the concept of irrationality is fundamental to understanding the real number system, which includes both rational and irrational numbers. Since √2 cannot be precisely expressed, we often estimate its value for practical purposes, understanding that this estimation is an approximation of the actual, infinitely non-repeating decimal expansion of the number.