Math Roots Worksheets - Free Printable

Let's solve each problem step by step.

We are given equations of the form:

$$
\sqrt{a} \times \boxed{\phantom{0}} = b
$$

Our goal is to find the missing number (the blank) in each equation. We'll do this by:

1. First, evaluate the square root.
2. Then divide the result on the right-hand side by that square root to find the missing multiplier.

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Left Column:

1. $ \sqrt{121} \times \boxed{} = 33 $

- $ \sqrt{121} = 11 $
- So: $ 11 \times x = 33 \Rightarrow x = 33 / 11 = 3 $

✔ Answer: 3

2. $ \sqrt{25} \times \boxed{} = 40 $

- $ \sqrt{25} = 5 $
- $ 5x = 40 \Rightarrow x = 8 $

✔ Answer: 8

3. $ \sqrt{9} \times \boxed{} = 6 $

- $ \sqrt{9} = 3 $
- $ 3x = 6 \Rightarrow x = 2 $

✔ Answer: 2

4. $ \sqrt{9} \times \boxed{} = 9 $

- $ \sqrt{9} = 3 $
- $ 3x = 9 \Rightarrow x = 3 $

✔ Answer: 3

5. $ \sqrt{64} \times \boxed{} = 32 $

- $ \sqrt{64} = 8 $
- $ 8x = 32 \Rightarrow x = 4 $

✔ Answer: 4

6. $ \sqrt{49} \times \boxed{} = 14 $

- $ \sqrt{49} = 7 $
- $ 7x = 14 \Rightarrow x = 2 $

✔ Answer: 2

7. $ \sqrt{196} \times \boxed{} = 28 $

- $ \sqrt{196} = 14 $
- $ 14x = 28 \Rightarrow x = 2 $

✔ Answer: 2

8. $ \sqrt{81} \times \boxed{} = 9 $

- $ \sqrt{81} = 9 $
- $ 9x = 9 \Rightarrow x = 1 $

✔ Answer: 1

9. $ \sqrt{36} \times \boxed{} = 120 $

- $ \sqrt{36} = 6 $
- $ 6x = 120 \Rightarrow x = 20 $

✔ Answer: 20

10. $ \sqrt{64} \times \boxed{} = 24 $

- $ \sqrt{64} = 8 $
- $ 8x = 24 \Rightarrow x = 3 $

✔ Answer: 3

11. $ \sqrt{225} \times \boxed{} = 30 $

- $ \sqrt{225} = 15 $
- $ 15x = 30 \Rightarrow x = 2 $

✔ Answer: 2

12. $ \sqrt{9} \times \boxed{} = 12 $

- $ \sqrt{9} = 3 $
- $ 3x = 12 \Rightarrow x = 4 $

✔ Answer: 4

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Right Column:

13. $ \sqrt{36} \times \boxed{} = 150 $

- $ \sqrt{36} = 6 $
- $ 6x = 150 \Rightarrow x = 25 $

✔ Answer: 25

14. $ \sqrt{25} \times \boxed{} = 20 $

- $ \sqrt{25} = 5 $
- $ 5x = 20 \Rightarrow x = 4 $

✔ Answer: 4

15. $ \sqrt{400} \times \boxed{} = 60 $

- $ \sqrt{400} = 20 $
- $ 20x = 60 \Rightarrow x = 3 $

✔ Answer: 3

16. $ \sqrt{49} \times \boxed{} = 56 $

- $ \sqrt{49} = 7 $
- $ 7x = 56 \Rightarrow x = 8 $

✔ Answer: 8

17. $ \sqrt{16} \times \boxed{} = 16 $

- $ \sqrt{16} = 4 $
- $ 4x = 16 \Rightarrow x = 4 $

✔ Answer: 4

18. $ \sqrt{100} \times \boxed{} = 20 $

- $ \sqrt{100} = 10 $
- $ 10x = 20 \Rightarrow x = 2 $

✔ Answer: 2

19. $ \sqrt{289} \times \boxed{} = 119 $

- $ \sqrt{289} = 17 $
- $ 17x = 119 \Rightarrow x = 7 $

✔ Answer: 7

20. $ \sqrt{16} \times \boxed{} = 40 $

- $ \sqrt{16} = 4 $
- $ 4x = 40 \Rightarrow x = 10 $

✔ Answer: 10

21. $ \sqrt{289} \times \boxed{} = 34 $

- $ \sqrt{289} = 17 $
- $ 17x = 34 \Rightarrow x = 2 $

✔ Answer: 2

22. $ \sqrt{144} \times \boxed{} = 60 $

- $ \sqrt{144} = 12 $
- $ 12x = 60 \Rightarrow x = 5 $

✔ Answer: 5

23. $ \sqrt{484} \times \boxed{} = 66 $

- $ \sqrt{484} = 22 $
- $ 22x = 66 \Rightarrow x = 3 $

✔ Answer: 3

24. $ \sqrt{9} \times \boxed{} = 15 $

- $ \sqrt{9} = 3 $
- $ 3x = 15 \Rightarrow x = 5 $

✔ Answer: 5

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Final Answers (in order):

Left Column:
1. 3
2. 8
3. 2
4. 3
5. 4
6. 2
7. 2
8. 1
9. 20
10. 3
11. 2
12. 4

Right Column:
13. 25
14. 4
15. 3
16. 8
17. 4
18. 2
19. 7
20. 10
21. 2
22. 5
23. 3
24. 5

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✔ All problems solved! Let me know if you'd like a printable version or explanation for any specific one.