Math worksheet for practicing division of square roots with multiple problems.

To solve these problems, we use the rule for dividing square roots:
$$ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} $$

This means you can divide the numbers inside the square roots first, and then find the square root of the result. If the result is a perfect square (like 4, 9, 16, 25, etc.), the answer will be a whole number. If not, we simplify the fraction or the radical.

Here is the step-by-step solution for each problem on the worksheet:

Left Column:

1. $\sqrt{125} \div \sqrt{5}$
* Divide inside: $125 \div 5 = 25$
* Square root: $\sqrt{25} = 5$

2. $\sqrt{48} \div \sqrt{12}$
* Divide inside: $48 \div 12 = 4$
* Square root: $\sqrt{4} = 2$

3. $\sqrt{2} \div \sqrt{8}$
* Combine: $\sqrt{\frac{2}{8}}$
* Simplify fraction: $\frac{2}{8} = \frac{1}{4}$
* Square root: $\sqrt{\frac{1}{4}} = \frac{1}{2}$

4. $\sqrt{8} \div \sqrt{2}$
* Divide inside: $8 \div 2 = 4$
* Square root: $\sqrt{4} = 2$

5. $\sqrt{72} \div \sqrt{2}$
* Divide inside: $72 \div 2 = 36$
* Square root: $\sqrt{36} = 6$

6. $\sqrt{80} \div \sqrt{5}$
* Divide inside: $80 \div 5 = 16$
* Square root: $\sqrt{16} = 4$

7. $\sqrt{108} \div \sqrt{3}$
* Divide inside: $108 \div 3 = 36$
* Square root: $\sqrt{36} = 6$

8. $\sqrt{50} \div \sqrt{2}$
* Divide inside: $50 \div 2 = 25$
* Square root: $\sqrt{25} = 5$

9. $\sqrt{25} \div \sqrt{400}$
* Divide inside: $25 \div 400 = \frac{25}{400}$
* Simplify fraction: $\frac{25}{400} = \frac{1}{16}$ (since $25 \times 16 = 400$)
* Square root: $\sqrt{\frac{1}{16}} = \frac{1}{4}$

10. $\sqrt{72} \div \sqrt{8}$
* Divide inside: $72 \div 8 = 9$
* Square root: $\sqrt{9} = 3$

11. $\sqrt{196} \div \sqrt{4}$
* Divide inside: $196 \div 4 = 49$
* Square root: $\sqrt{49} = 7$

12. $\sqrt{90} \div \sqrt{10}$
* Divide inside: $90 \div 10 = 9$
* Square root: $\sqrt{9} = 3$

Right Column:

13. $\sqrt{15} \div \sqrt{375}$
* Combine: $\sqrt{\frac{15}{375}}$
* Simplify fraction: $375 \div 15 = 25$, so $\frac{15}{375} = \frac{1}{25}$
* Square root: $\sqrt{\frac{1}{25}} = \frac{1}{5}$

14. $\sqrt{99} \div \sqrt{11}$
* Divide inside: $99 \div 11 = 9$
* Square root: $\sqrt{9} = 3$

15. $\sqrt{245} \div \sqrt{5}$
* Divide inside: $245 \div 5 = 49$
* Square root: $\sqrt{49} = 7$

16. $\sqrt{13} \div \sqrt{52}$
* Combine: $\sqrt{\frac{13}{52}}$
* Simplify fraction: $52 \div 13 = 4$, so $\frac{13}{52} = \frac{1}{4}$
* Square root: $\sqrt{\frac{1}{4}} = \frac{1}{2}$

17. $\sqrt{15} \div \sqrt{60}$
* Combine: $\sqrt{\frac{15}{60}}$
* Simplify fraction: $60 \div 15 = 4$, so $\frac{15}{60} = \frac{1}{4}$
* Square root: $\sqrt{\frac{1}{4}} = \frac{1}{2}$

18. $\sqrt{432} \div \sqrt{3}$
* Divide inside: $432 \div 3 = 144$
* Square root: $\sqrt{144} = 12$

19. $\sqrt{640} \div \sqrt{40}$
* Divide inside: $640 \div 40 = 16$
* Square root: $\sqrt{16} = 4$

20. $\sqrt{50} \div \sqrt{200}$
* Combine: $\sqrt{\frac{50}{200}}$
* Simplify fraction: $\frac{50}{200} = \frac{5}{20} = \frac{1}{4}$
* Square root: $\sqrt{\frac{1}{4}} = \frac{1}{2}$

21. $\sqrt{128} \div \sqrt{8}$
* Divide inside: $128 \div 8 = 16$
* Square root: $\sqrt{16} = 4$

22. $\sqrt{288} \div \sqrt{32}$
* Divide inside: $288 \div 32 = 9$
* Square root: $\sqrt{9} = 3$

23. $\sqrt{200} \div \sqrt{8}$
* Divide inside: $200 \div 8 = 25$
* Square root: $\sqrt{25} = 5$

24. $\sqrt{8} \div \sqrt{32}$
* Combine: $\sqrt{\frac{8}{32}}$
* Simplify fraction: $\frac{8}{32} = \frac{1}{4}$
* Square root: $\sqrt{\frac{1}{4}} = \frac{1}{2}$

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

Right Column:
13. 1/5
14. 3
15. 7
16. 1/2
17. 1/2
18. 12
19. 4
20. 1/2
21. 4
22. 3
23. 5
24. 1/2