1. Problem Q10a: Find the HCF of 72, 64, and 24. Step 1: Prime factorize each number. - 72 = $2^3 \times 3^2$ - 64 = $2^6$ - 24 = $2^3 \times 3$ Step 2: Identify the common prime factors with the lowest powers. - Common prime factor is 2. - Minimum power of 2 is $2^3$. Step 3: Calculate HCF. - HCF = $2^3 = 8$ 2. Problem Q10b: Find the LCM of 72, 64, and 24. Step 1: Use the prime factorizations from above. - 72 = $2^3 \times 3^2$ - 64 = $2^6$ - 24 = $2^3 \times 3$ Step 2: Take the highest power of each prime. - For 2, highest power is $2^6$ (from 64). - For 3, highest power is $3^2$ (from 72). Step 3: Calculate LCM. - LCM = $2^6 \times 3^2 = 64 \times 9 = 576$ 3. Problem Q11i: Evaluate the squares. i) $(-6)^2 = 36$ ii) $(-1.3)^2 = 1.69$ iii) $(-2.9)^2 = 8.41$ 4. Problem Q11ii: Evaluate the square roots. i) $\sqrt{17.64} = 4.2$ ii) $\sqrt{26.01} = 5.1$ iii) $\sqrt{13.69} = 3.7$