Question

Which of the following numbers are irrational numbers?
1) 0.45
2) 8π²
3) 144

Answer 1

Out of the given numbers, 0.45 and 144 are rational numbers because they can be expressed as fractions. The number 8π² is irrational because π is an irrational number, and multiplying it by any rational number results in an irrational number.

Step-by-step explanation:

The student is asking which of the three numbers are irrational: 1) 0.45, 2) 8π², 3) 144.

An irrational number is a number that cannot be expressed as a simple fraction - that is, the decimal goes on forever without repeating. Here's a look at the three numbers:

1. 0.45 is a rational number as it can be expressed as a fraction, 45/100.
2. 8π² is an irrational number because π (pi) is an irrational number, meaning it has an infinite number of decimals that do not repeat. Multiplying π by any rational number will result in an irrational number.
3. 144 is a rational number because it is an integer, and all integers are rational numbers as they can be expressed as the fraction 144/1.

Therefore, out of the given options, the number 8π² is an irrational number.