Square root estimation problems using factor trees, rounded to the nearest tenth.

1. √63
- Factor tree: 63 → 9 × 7 → 3 × 3 × 7
- Simplify: √(3² × 7) = 3√7
- Approximate: 3 × 2.64575 ≈ 7.937 → 7.9

2. √45
- Factor tree: 45 → 9 × 5 → 3 × 3 × 5
- Simplify: √(3² × 5) = 3√5
- Approximate: 3 × 2.23607 ≈ 6.708 → 6.7

3. √170
- Factor tree: 170 → 10 × 17 → 2 × 5 × 17
- Cannot simplify (no perfect square factors >1)
- Approximate: √170 ≈ 13.038 → 13.0

4. √130
- Factor tree: 130 → 10 × 13 → 2 × 5 × 13
- Cannot simplify (no perfect square factors >1)
- Approximate: √130 ≈ 11.402 → 11.4

5. √2
- Factor tree: 2 → prime
- Cannot simplify
- Approximate: √2 ≈ 1.414 → 1.4

6. √20
- Factor tree: 20 → 4 × 5 → 2 × 2 × 5
- Simplify: √(2² × 5) = 2√5
- Approximate: 2 × 2.23607 ≈ 4.472 → 4.5