(a) 6 144 63 11 288 72 8
From the list, write down
(i) the multiple of 7,
(ii) the cube of 2,
(iii) the prime number,
(iv) the lowest common multiple (LCM) of 16 and 18.
(b) Without using a calculator explain why the square of 4.86 must be between 16 and 25.
(c) Find the value of
(i) \(4^7\)
(ii) \(12^0\)
(iii) \(8.3^2 + \sqrt{27}\)
(d) Write 90 as the product of its prime factors.
▶️ Answer/Explanation
(a)
(i) Ans: 63 – 63 ÷ 7 = 9 exactly
(ii) Ans: 8 – 2³ = 8
(iii) Ans: 11 – Only number divisible by 1 and itself
(iv) Ans: 144 – LCM of 16 (2⁴) and 18 (2×3²) is 2⁴×3² = 144
(b) Explanation:
4.86 is between 4 and 5. Since 4² = 16 and 5² = 25, and squaring preserves order, 4.86² must be between 16 and 25.
(c)
(i) Ans: 16,384 – \(4^7 = 4 × 4 × 4 × 4 × 4 × 4 × 4 = 16,384\)
(ii) Ans: 1 – Any non-zero number to power 0 equals 1
(iii) Ans: 74.09 – \(8.3^2 = 68.89\), \(\sqrt{27} ≈ 5.196\), sum ≈ 74.09
(d) Ans: \(2 × 3^2 × 5\)
Prime factorization:
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Thus, 90 = 2 × 3 × 3 × 5 = \(2 × 3^2 × 5\)