QUESTION 1 1.1 Given the list of numbers: \( \sqrt{1296} ; \frac{33}{3} ; 0.21 ; \pi ; 36 ; \sqrt{14} \). write down at least two of the following. 1.1.1 Rational numbers \( \qquad \) (1) 1.1.2 Integers \( \qquad \) (1) 1.1.3 Multiples of 6 \( \qquad \) (1) 1.1.4 Irrational numbers. (1) 1.2 Find the LCM and HCF of the following values by using prime factorization: \( \mathbf{7 2} \) and \( \mathbf{1 8 0} \). (4) 1.3 The ratio of boys to girls at a party is \( 4: 5 \). If there are 20 boys, how many girls are there? (2) 1.4 Thato runs 10 km in 30 minutes. how long (in minutes) will it take him to run 50 km ? (2) \( \square \) [12]

Rational numbers in your list include \( \frac{33}{3} = 11 \) and \( 36 \), both of which can be expressed as the ratio of two integers. Meanwhile, for the integers, \( 11 \) and \( 36 \) are whole numbers that fit the criteria. As far as multiples of 6 go, \( 36 \) meets the mark, and so does \( 0.21 \) since it’s expressed as \( \frac{21}{100} \), which isn't a multiple of 6 but is intriguing! Irrational numbers like \( \pi \) and \( \sqrt{14} \) can’t be expressed as fractions, making them quite fascinating! Now, moving on to prime factorization! For 72, we break it down to \( 2^3 \times 3^2 \) and for 180, we get \( 2^2 \times 3^2 \times 5^1 \). The highest common factor (HCF) is \( 2^2 \times 3^2 = 36 \), while the least common multiple (LCM) is \( 2^3 \times 3^2 \times 5^1 = 360 \). It's like a little number dance, where the primes come together to find common ground! With a ratio of \( 4:5 \) and \( 20 \) boys, we can represent the number of girls as \( \frac{5}{4} \times 20 = 25 \). Thus, there are 25 lucky girls joining the party! And, if Thato runs 10 km in 30 minutes, for 50 km he’d take \( \frac{50}{10} \times 30 = 150 \) minutes — a brisk pace indeed!