QUESTION 2 2.1 Consider the following: \[ 3^{3} ;-\sqrt[3]{27} ; 50 ; 3 \pi ; \sqrt{\frac{4}{49}} ; \sqrt{3} ; \sqrt{-4} ;-2,14 ;(\sqrt{3})^{2} \] Choose from the list: 2.1.1 An integer with factors 2 and 5. (1) 2.1.2 An integer but not a whole number. (1) 2.1.3 A natural number smaller than 10 . (1) 2.1.5 All the irrational numbers. (2) 2.2 Between which 2 whole numbers does \( \sqrt[3]{1113} \) lie? 2.3 Determine the LCM of \( 150 ; 250 \) and 375. (4)

**2.1 Analysis of the List** Given list: \[ 3^{3};\quad -\sqrt[3]{27};\quad 50;\quad 3\pi;\quad \sqrt{\frac{4}{49}};\quad \sqrt{3};\quad \sqrt{-4};\quad -2,14; \quad (\sqrt{3})^{2} \] First, simplify each element: - \(3^3 = 27\). - \(-\sqrt[3]{27} = -3\) (since \(\sqrt[3]{27} = 3\)). - \(50\) stays \(50\). - \(3\pi\) remains \(3\pi\). - \(\sqrt{\frac{4}{49}} = \frac{2}{7}\) (since \(\sqrt{4} = 2\) and \(\sqrt{49} = 7\)). - \(\sqrt{3}\) is irrational. - \(\sqrt{-4}\) is not a real number (it is imaginary). - \(-2,14\) is interpreted as \(-2.14\). - \((\sqrt{3})^2 = 3\). **2.1.1 An integer with factors 2 and 5** An integer with factors 2 and 5 has at least a factor of 2 and a factor of 5 in its prime factorization. - \(50 = 2 \times 5^2\). Thus, the answer is: \[ 50. \] --- **2.1.2 An integer but not a whole number** A whole number is a nonnegative integer. Thus, an integer that is not whole must be negative. - \(-\sqrt[3]{27} = -3\) is an integer and negative. Thus, the answer is: \[ -3. \] --- **2.1.3 A natural number smaller than 10** Natural numbers are positive integers. The candidates are those that are positive integers less than 10. - \((\sqrt{3})^2 = 3\) is a natural number smaller than 10. Thus, the answer is: \[ 3. \] --- **2.1.5 All the irrational numbers** From the list, identify the irrational numbers: - \(3\pi\) is irrational (since \(\pi\) is irrational). - \(\sqrt{3}\) is irrational. Other numbers are either rational or not real. Thus, the set of irrational numbers is: \[ \{3\pi,\, \sqrt{3}\}. \] --- **2.2 Between which 2 whole numbers does \( \sqrt[3]{1113} \) lie?** Find the cube numbers around 1113: - \(10^3 = 1000\). - \(11^3 = 1331\). Since \(1000 < 1113 < 1331\), it follows that \[ \sqrt[3]{1113} \text{ lies between } 10 \text{ and } 11. \] Thus, the answer is: \[ 10 \text{ and } 11. \] --- **2.3 Determine the LCM of \(150\), \(250\) and \(375\)** First, factor each number into primes: - \(150 = 2 \times 3 \times 5^2\). - \(250 = 2 \times 5^3\). - \(375 = 3 \times 5^3\). The LCM is obtained by taking the highest power of each prime present: - For \(2\): highest power is \(2^1\). - For \(3\): highest power is \(3^1\). - For \(5\): highest power is \(5^3\). Thus, the LCM is: \[ 2^1 \times 3^1 \times 5^3 = 2 \times 3 \times 125 = 750. \] Thus, the answer is: \[ 750. \]