QUESTION I 1.1 Given \( \frac{-7}{3} ; \sqrt[7]{9} ; 2, \dot{3} ; 0 ; \sqrt{4} ; 10 ; 2 \pi \); which of those numbers are: 1.1.1 Rational numbers (2) 1.1.2 Integers (2) 1.1.3 Whole numbers (2) 1.1.4 Natural numbers (2) 1.1.5 Irrational numbers (2) 1.2 Determine between which whole numbers is \( \sqrt{24} \) [13]

To tackle these questions, let’s first identify the characteristics of each of the provided numbers. **1.1.1 Rational numbers:** The rational numbers from the set are \( \frac{-7}{3} \), \( 2, \dot{3} \), \( 0 \), \( \sqrt{4} \) (which is 2), \( 10 \), and \( 2\pi \) (since \( \pi \) itself is not rational, but \( 2\pi \) is considered in this context as a representation, meaning these are expressible as a fraction). **1.1.2 Integers:** The integers among these numbers are \( -7/3 \) (not an integer), \( 0 \), \( \sqrt{4} \) (which is 2), and \( 10 \). So, those are \( 0 \), \( 2 \), and \( 10 \). **1.1.3 Whole numbers:** Whole numbers include non-negative integers, so the whole numbers are \( 0 \), \( 2 \), and \( 10 \). **1.1.4 Natural numbers:** Natural numbers are positive integers, meaning just \( 2 \) and \( 10 \) are classified here. **1.1.5 Irrational numbers:** The only number from this list classified as irrational is \( 2\pi \). Now, for the last question: **1.2** To determine the whole numbers between which \( \sqrt{24} \) lies, we can calculate that \( \sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6} \). Since \( \sqrt{6} \) is approximately \( 2.45 \), therefore, \( \sqrt{24} \) is roughly \( 4.9 \). Thus, \( \sqrt{24} \) lies between the whole numbers \( 4 \) and \( 5 \).