Free Collection Of Estimating Square Roots Worksheets - Free Printable

Let's solve each problem step by step.

We are asked to determine which two whole numbers the square root lies between for each given number. This means we need to find two consecutive whole numbers such that:

$$
a < \sqrt{n} < b
$$

where $ a $ and $ b $ are consecutive whole numbers, and $ a^2 < n < b^2 $.

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Step-by-step approach:

1. Find perfect squares near the given number.
2. Identify the two perfect squares between which the number lies.
3. Take their square roots — those will be the two whole numbers.

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Now let’s go through each one:

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1) √76
- $ 8^2 = 64 $, $ 9^2 = 81 $
- $ 64 < 76 < 81 $ → √76 is between 8 and 9

2) √94
- $ 9^2 = 81 $, $ 10^2 = 100 $
- $ 81 < 94 < 100 $ → √94 is between 9 and 10

3) √50
- $ 7^2 = 49 $, $ 8^2 = 64 $
- $ 49 < 50 < 64 $ → √50 is between 7 and 8

4) √26
- $ 5^2 = 25 $, $ 6^2 = 36 $
- $ 25 < 26 < 36 $ → √26 is between 5 and 6

5) √45
- $ 6^2 = 36 $, $ 7^2 = 49 $
- $ 36 < 45 < 49 $ → √45 is between 6 and 7

6) √13
- $ 3^2 = 9 $, $ 4^2 = 16 $
- $ 9 < 13 < 16 $ → √13 is between 3 and 4

7) √78
- $ 8^2 = 64 $, $ 9^2 = 81 $
- $ 64 < 78 < 81 $ → √78 is between 8 and 9

8) √74
- $ 8^2 = 64 $, $ 9^2 = 81 $
- $ 64 < 74 < 81 $ → √74 is between 8 and 9

9) √35
- $ 5^2 = 25 $, $ 6^2 = 36 $
- $ 25 < 35 < 36 $ → √35 is between 5 and 6

10) √58
- $ 7^2 = 49 $, $ 8^2 = 64 $
- $ 49 < 58 < 64 $ → √58 is between 7 and 8

11) √99
- $ 9^2 = 81 $, $ 10^2 = 100 $
- $ 81 < 99 < 100 $ → √99 is between 9 and 10

12) √73
- $ 8^2 = 64 $, $ 9^2 = 81 $
- $ 64 < 73 < 81 $ → √73 is between 8 and 9

13) √80
- $ 8^2 = 64 $, $ 9^2 = 81 $
- $ 64 < 80 < 81 $ → √80 is between 8 and 9

14) √24
- $ 4^2 = 16 $, $ 5^2 = 25 $
- $ 16 < 24 < 25 $ → √24 is between 4 and 5

15) √89
- $ 9^2 = 81 $, $ 10^2 = 100 $
- $ 81 < 89 < 100 $ → √89 is between 9 and 10

16) √53
- $ 7^2 = 49 $, $ 8^2 = 64 $
- $ 49 < 53 < 64 $ → √53 is between 7 and 8

17) √87
- $ 9^2 = 81 $, $ 10^2 = 100 $
- $ 81 < 87 < 100 $ → √87 is between 9 and 10

18) √60
- $ 7^2 = 49 $, $ 8^2 = 64 $
- $ 49 < 60 < 64 $ → √60 is between 7 and 8

19) √79
- $ 8^2 = 64 $, $ 9^2 = 81 $
- $ 64 < 79 < 81 $ → √79 is between 8 and 9

20) √37
- $ 6^2 = 36 $, $ 7^2 = 49 $
- $ 36 < 37 < 49 $ → √37 is between 6 and 7

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Final Answers:

| # | Answer (between) |
|---|------------------|
| 1 | 8, 9 |
| 2 | 9, 10 |
| 3 | 7, 8 |
| 4 | 5, 6 |
| 5 | 6, 7 |
| 6 | 3, 4 |
| 7 | 8, 9 |
| 8 | 8, 9 |
| 9 | 5, 6 |
|10 | 7, 8 |
|11 | 9, 10 |
|12 | 8, 9 |
|13 | 8, 9 |
|14 | 4, 5 |
|15 | 9, 10 |
|16 | 7, 8 |
|17 | 9, 10 |
|18 | 7, 8 |
|19 | 8, 9 |
|20 | 6, 7 |

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✔ Answer Key (for the "Answers" column):

1. 8, 9
2. 9, 10
3. 7, 8
4. 5, 6
5. 6, 7
6. 3, 4
7. 8, 9
8. 8, 9
9. 5, 6
10. 7, 8
11. 9, 10
12. 8, 9
13. 8, 9
14. 4, 5
15. 9, 10
16. 7, 8
17. 9, 10
18. 7, 8
19. 8, 9
20. 6, 7

Let me know if you'd like this in a printable format or with explanations for each!