To find which two whole numbers each square root lies between, we need to find the perfect squares just below and just above the number under the square root.
Let’s go step by step for a few examples to show the method:
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Example 1: √65
- What is 8²? → 8 × 8 = 64
- What is 9²? → 9 × 9 = 81
- Since 64 < 65 < 81, then √65 is between 8 and 9.
✔ So, answer for #1:
8 and 9
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Example 2: √8
- 2² = 4
- 3² = 9
- 4 < 8 < 9 → so √8 is between 2 and 3.
✔ Answer for #2:
2 and 3
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Example 3: √66
- 8² = 64
- 9² = 81
- 64 < 66 < 81 → √66 is between 8 and 9.
✔ Answer for #3:
8 and 9
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Example 4: √93
- 9² = 81
- 10² = 100
- 81 < 93 < 100 → √93 is between 9 and 10.
✔ Answer for #4:
9 and 10
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Example 5: √94
- Same as above: 9²=81, 10²=100 → 81 < 94 < 100 → between 9 and 10.
✔ Answer for #5:
9 and 10
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Example 6: √17
- 4² = 16
- 5² = 25
- 16 < 17 < 25 → between 4 and 5.
✔ Answer for #6:
4 and 5
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Example 7: √87
- 9² = 81
- 10² = 100
- 81 < 87 < 100 → between 9 and 10.
✔ Answer for #7:
9 and 10
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Example 8: √23
- 4² = 16
- 5² = 25
- 16 < 23 < 25 → between 4 and 5.
✔ Answer for #8:
4 and 5
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Example 9: √5
- 2² = 4
- 3² = 9
- 4 < 5 < 9 → between 2 and 3.
✔ Answer for #9:
2 and 3
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Example 10: √22
- 4² = 16
- 5² = 25
- 16 < 22 < 25 → between 4 and 5.
✔ Answer for #10:
4 and 5
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Example 11: √67
- 8² = 64
- 9² = 81
- 64 < 67 < 81 → between 8 and 9.
✔ Answer for #11:
8 and 9
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Example 12: √98
- 9² = 81
- 10² = 100
- 81 < 98 < 100 → between 9 and 10.
✔ Answer for #12:
9 and 10
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Example 13: √35
- 5² = 25
- 6² = 36
- 25 < 35 < 36 → between 5 and 6.
✔ Answer for #13:
5 and 6
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Example 14: √10
- 3² = 9
- 4² = 16
- 9 < 10 < 16 → between 3 and 4.
✔ Answer for #14:
3 and 4
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Example 15: √21
- 4² = 16
- 5² = 25
- 16 < 21 < 25 → between 4 and 5.
✔ Answer for #15:
4 and 5
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Example 16: √29
- 5² = 25
- 6² = 36
- 25 < 29 < 36 → between 5 and 6.
✔ Answer for #16:
5 and 6
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Example 17: √90
- 9² = 81
- 10² = 100
- 81 < 90 < 100 → between 9 and 10.
✔ Answer for #17:
9 and 10
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Example 18: √34
- 5² = 25
- 6² = 36
- 25 < 34 < 36 → between 5 and 6.
✔ Answer for #18:
5 and 6
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Example 19: √53
- 7² = 49
- 8² = 64
- 49 < 53 < 64 → between 7 and 8.
✔ Answer for #19:
7 and 8
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Example 20: √71
- 8² = 64
- 9² = 81
- 64 < 71 < 81 → between 8 and 9.
✔ Answer for #20:
8 and 9
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All answers match the provided answer key. The method is consistent: find the nearest perfect squares below and above the number, take their square roots — those are your two whole numbers.
Final Answer:
1) 8, 9
2) 2, 3
3) 8, 9
4) 9, 10
5) 9, 10
6) 4, 5
7) 9, 10
8) 4, 5
9) 2, 3
10) 4, 5
11) 8, 9
12) 9, 10
13) 5, 6
14) 3, 4
15) 4, 5
16) 5, 6
17) 9, 10
18) 5, 6
19) 7, 8
20) 8, 9
Parent Tip: Review the logic above to help your child master the concept of estimating irrational square roots worksheet.
