Square Numbers & Square Roots — Solutions

1. Calculate Square Numbers

   1. 1²: 1 ▶ View Solution
   2. 2²: 4 ▶ View Solution
   3. 3²: 9 ▶ View Solution
   4. 4²: 16 ▶ View Solution
   5. 5²: 25 ▶ View Solution
   6. 6²: 36 ▶ View Solution
   7. 7²: 49 ▶ View Solution
   8. 8²: 64 ▶ View Solution

2. Find Square Roots of Perfect Squares

   1. √1: 1 ▶ View Solution
   2. √4: 2 ▶ View Solution
   3. √9: 3 ▶ View Solution
   4. √16: 4 ▶ View Solution
   5. √25: 5 ▶ View Solution
   6. √36: 6 ▶ View Solution
   7. √49: 7 ▶ View Solution
   8. √64: 8 ▶ View Solution

3. Identify Perfect Squares

   1. Perfect squares from list: 9, 16, 25, 36, 49 ▶ View Solution
   2. Is 50 a perfect square?: No — between 7² = 49 and 8² = 64 ▶ View Solution
   3. Is 100 a perfect square?: Yes — 10² = 100 ▶ View Solution
   4. Is 200 a perfect square?: No — between 14² = 196 and 15² = 225 ▶ View Solution
   5. Perfect squares between 50 and 150: 64, 81, 100, 121, 144 ▶ View Solution

4. Estimate Square Roots

   1. √50: between 7 and 8 ▶ View Solution
   2. √20: between 4 and 5 ▶ View Solution
   3. √80: between 8 and 9 ▶ View Solution
   4. √130: between 11 and 12 ▶ View Solution
   5. √200: between 14 and 15 ▶ View Solution
   6. √75: between 8 and 9 ▶ View Solution
   7. √45: between 6 and 7 ▶ View Solution
   8. √110: between 10 and 11 ▶ View Solution

5. Squaring and Square Rooting as Inverse Operations

   1. √(6²): 6 ▶ View Solution
   2. (√49)²: 49 ▶ View Solution
   3. √(n²) = n for all positive integers: True ▶ View Solution
   4. (√n)² = n for all perfect squares: True ▶ View Solution
   5. Explain the relationship: Squaring and square rooting are inverse operations — each undoes the other ▶ View Solution

6. Problem Solving with Square Numbers and Roots

   1. Side of 49 m² square: 7 m ▶ View Solution
   2. Side of 144 cm² square: 12 cm ▶ View Solution
   3. 900 cm² floor with 25 cm² tiles: 36 tiles ▶ View Solution
   4. Hypotenuse with legs 3 cm and 4 cm: 5 cm ▶ View Solution
   5. Square with 60 m perimeter, find area: 225 m² ▶ View Solution

7. Cube Numbers

   1. 1³: 1 ▶ View Solution
   2. 2³: 8 ▶ View Solution
   3. 3³: 27 ▶ View Solution
   4. 4³: 64 ▶ View Solution
   5. 5³: 125 ▶ View Solution
   6. 6³: 216 ▶ View Solution
   7. 7³: 343 ▶ View Solution
   8. 8³: 512 ▶ View Solution

8. Squares and Roots — Mixed Table

   1. 9²: 81 ▶ View Solution
   2. √100: 10 ▶ View Solution
   3. 11²: 121 ▶ View Solution
   4. √144: 12 ▶ View Solution
   5. 10²: 100 ▶ View Solution
   6. √121: 11 ▶ View Solution
   7. 12²: 144 ▶ View Solution
   8. √169: 13 ▶ View Solution

9. Pythagoras Connection

   1. c² = 6² + 8²: 10 ▶ View Solution
   2. c² = 5² + 12²: 13 ▶ View Solution
   3. c² = 8² + 15²: 17 ▶ View Solution
   4. a² = 10² − 6²: 8 ▶ View Solution
   5. b² = 13² − 5²: 12 ▶ View Solution

10. Real-World Problem Solving with Squares and Roots

    1. Side of 196 m² square: 14 m ▶ View Solution
    2. Side and perimeter of 2 500 m² field: 50 m side; 200 m perimeter ▶ View Solution
    3. Square with 280 cm perimeter, find area: 4 900 cm² ▶ View Solution
    4. Side and diagonal of 2 025 cm² square: 45 cm side; diagonal ≈ 63.5 cm ▶ View Solution