Question

1. which of the following best describes the set of numbers to which √2 belongs? a. imaginary b. irrational c. rational d. natural

Explanation:

Step1: Recall number - type definitions

A natural number is a positive integer (1, 2, 3, ...). A rational number is a number that can be written as $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. An irrational number cannot be written as a fraction of two integers. An imaginary number is of the form $bi$ where $b$ is a non - zero real number and $i=\sqrt{- 1}$.

Step2: Analyze $\sqrt{2}$

$\sqrt{2}$ cannot be written as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers. So it is not a rational number. Also, $\sqrt{2}\approx1.414$, it is a real number (not of the form $bi$ so not imaginary), and it is not a positive integer (so not natural). Since it cannot be written as a ratio of two integers, it is an irrational number.

Answer:

B. irrational