Topic Review — Indices & Square Numbers — Solutions

1. Index Notation — Write and Evaluate

   1. 5 × 5 × 5 × 5 = 5⁴ ▶ View Solution
   2. 2 × 2 × 2 × 2 × 2 = 2⁵ ▶ View Solution
   3. 3⁴ = 81 ▶ View Solution
   4. 2⁷ = 128 ▶ View Solution
   5. 10⁴ = 10 000 ▶ View Solution
   6. 6³ = 6 × 6 × 6 = 216 ▶ View Solution
   7. 5⁰ = 1 ▶ View Solution
   8. 9¹ = 9 ▶ View Solution

2. Square Numbers and Square Roots

   1. 11² = 121 ▶ View Solution
   2. 13² = 169 ▶ View Solution
   3. √64 = 8 ▶ View Solution
   4. √196 = 14 ▶ View Solution
   5. Is 150 a perfect square? No — 12²=144, 13²=169. 150 lies between them. ▶ View Solution
   6. √60 lies between: 7 and 8 (7²=49, 8²=64) ▶ View Solution
   7. √150 lies between: 12 and 13 (12²=144, 13²=169) ▶ View Solution

3. Prime Factorisation

   1. 24 = 2³ × 3 ▶ View Solution
   2. 60 = 2² × 3 × 5 ▶ View Solution
   3. 36 = 2² × 3² ▶ View Solution
   4. 100 = 2² × 5² ▶ View Solution
   5. 41 is prime or composite? Prime — it has no factors other than 1 and 41. ▶ View Solution
   6. Primes between 20 and 40: 23, 29, 31, 37 ▶ View Solution

4. HCF, LCM and Number Laws

   1. HCF(18, 24): 18 = 2×3², 24 = 2³×3. HCF = 2×3 = 6 ▶ View Solution
   2. LCM(6, 9): 6 = 2×3, 9 = 3². LCM = 2×3² = 18 ▶ View Solution
   3. 5² = 2⁵? False. 5²=25, 2⁵=32. They are not equal. ▶ View Solution
   4. Law in 7×(10+4)=7×10+7×4: Distributive Law ▶ View Solution
   5. Law in (3+9)+1=3+(9+1): Associative Law of Addition ▶ View Solution
   6. 15 ÷ 3 = 3 ÷ 15? False. 15÷3 = 5, but 3÷15 = 0.2. Division is not commutative. ▶ View Solution
   7. 8 × 99 mentally: 8×(100−1) = 800−8 = 792 ▶ View Solution

5. Comparing and Reasoning with Powers

   1. 4³ vs 3⁴: 4³=64, 3⁴=81. So 3⁴ is larger. ▶ View Solution
   2. √(10²) = 10. Squaring and taking the square root are inverse operations. ▶ View Solution
   3. 2³ × 5² = 8 × 25 = 200 ▶ View Solution
   4. Why 2¹⁰ ≠ 20: 2¹⁰ means 2 multiplied by itself 10 times = 1024. It does not mean 2×10. ▶ View Solution
   5. Square with area 169 cm²: Side = √169 = 13 cm. Perimeter = 4×13 = 52 cm. ▶ View Solution

6. Problem Solving — Mixed

   1. Bacteria tripling for 5 hours: 3⁵ = 243 bacteria ▶ View Solution
   2. Traffic lights next together: LCM(18, 24): 18=2×3², 24=2³×3. LCM=2³×3²=72 seconds ▶ View Solution
   3. (4×25)×17 = 100×17 = 1700 (using commutative and associative laws) ▶ View Solution
   4. Fencing square paddock: Side = √225 = 15 m. Perimeter = 60 m. Cost = 60×$12 = $720. ▶ View Solution
   5. 3⁴ vs 4³: 3⁴ = 3×3×3×3 = 81. 4³ = 4×4×4 = 64. They are not equal. 3⁴ is larger by 17. ▶ View Solution