Question

question 1 which of the following numbers is an irrational number? -5, √3, 1.5, 4

Explanation:

Step1: Recall definition of irrational numbers

Irrational numbers cannot be written as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b
eq0$.

Step2: Analyze each number

• $4$ is an integer and can be written as $\frac{4}{1}$, so it is rational.
• $1.5=\frac{3}{2}$, so it is rational.
• $\sqrt{3}$ cannot be written as a fraction of two integers. Its decimal - expansion is non - repeating and non - terminating. So it is irrational.
• $- 5$ is an integer and can be written as $\frac{-5}{1}$, so it is rational.

Answer:

$\sqrt{3}$