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Year 7 Maths • AC9M7N01 • Homework

Perfect Squares and Square Roots

Show enough working to make your reasoning clear. The questions cover all five curriculum elaborations.

8
Core questions
4
Reasoning questions
E1–E5
Complete coverage

Part A

Core understanding

  1. Draw or describe a square array for 8², then calculate 8².

  2. Write the inverse square-root fact for 15² = 225.

  3. Use 32 = 30 + 2 and an area model to calculate 32².

  4. Place √85 between consecutive whole numbers. Justify your bounds.

  5. Write the first differences and second differences for 1, 4, 9, 16, 25.

  6. Explain why a perfect square cannot end in 8.

  7. A square tiled floor contains 196 tiles. Find its side length and perimeter in tile lengths.

  8. A square has perimeter 60 cm. Find its area.

Part B

Reasoning and application

  1. A student writes 27² = 20² + 7². Explain the error and calculate 27² correctly.

  2. Without multiplying 24 × 24, use 23² = 529 and the pattern of odd differences to find 24².

  3. A square lawn has area 400 m². A path 2 m wide is built inside along all four edges. Find the remaining lawn area.

  4. A square storage area must cover at least 300 m² and have a whole-number side length. Find the shortest possible side and the resulting area.

Answer check
  1. 64
  2. √225 = 15
  3. 30² + 2×30×2 + 2² = 1024
  4. 9 < √85 < 10
  5. First: 3,5,7,9; second: 2,2,2
  6. Squares of final digits 0–9 never end in 8
  7. Side 14; perimeter 56
  8. Side 15; area 225 cm²
  9. Two 20-by-7 cross regions were omitted; 729
  10. Add 47; 576
  11. Inner side 16 m; area 256 m²
  12. 18 m; 324 m²

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