Final Answer:
√3 ≈ 1.7, √7 ≈ 2.6, √10 ≈ 3.2, √22 ≈ 4.7, √40 ≈ 6.3, √80 ≈ 8.9, √98 ≈ 9.9
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Explanation:
We need to estimate where each square root falls on the number line from 0 to 10.
First, remember some perfect squares:
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
- 6² = 36
- 7² = 49
- 8² = 64
- 9² = 81
- 10² = 100
Now estimate each root:
1. √3: Between √1 = 1 and √4 = 2. Since 3 is closer to 4, √3 ≈ 1.7
2. √7: Between √4 = 2 and √9 = 3. 7 is closer to 9, so √7 ≈ 2.6
3. √10: Between √9 = 3 and √16 = 4. 10 is just a bit more than 9, so √10 ≈ 3.2
4. √22: Between √16 = 4 and √25 = 5. 22 is closer to 25, so √22 ≈ 4.7
5. √40: Between √36 = 6 and √49 = 7. 40 is closer to 36, so √40 ≈ 6.3
6. √80: Between √64 = 8 and √81 = 9. 80 is very close to 81, so √80 ≈ 8.9
7. √98: Between √81 = 9 and √100 = 10. 98 is very close to 100, so √98 ≈ 9.9
So on the number line, mark them roughly at those decimal positions.
Parent Tip: Review the logic above to help your child master the concept of estimating irrational square roots worksheet.