Math worksheet for practicing division of square roots, featuring multiple problems and blank spaces for answers.

Let's solve each of these square root division problems step by step. The key rule we use is:

$$
\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}
$$

We can simplify the fraction under the square root and then simplify the square root if possible.

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Left Column:

1. $\sqrt{125} \div \sqrt{5} = \sqrt{\frac{125}{5}} = \sqrt{25} = 5$

2. $\sqrt{48} \div \sqrt{12} = \sqrt{\frac{48}{12}} = \sqrt{4} = 2$

3. $\sqrt{2} \div \sqrt{8} = \sqrt{\frac{2}{8}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$

4. $\sqrt{8} \div \sqrt{2} = \sqrt{\frac{8}{2}} = \sqrt{4} = 2$

5. $\sqrt{72} \div \sqrt{2} = \sqrt{\frac{72}{2}} = \sqrt{36} = 6$

6. $\sqrt{80} \div \sqrt{5} = \sqrt{\frac{80}{5}} = \sqrt{16} = 4$

7. $\sqrt{108} \div \sqrt{3} = \sqrt{\frac{108}{3}} = \sqrt{36} = 6$

8. $\sqrt{50} \div \sqrt{2} = \sqrt{\frac{50}{2}} = \sqrt{25} = 5$

9. $\sqrt{25} \div \sqrt{400} = \sqrt{\frac{25}{400}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$

10. $\sqrt{72} \div \sqrt{8} = \sqrt{\frac{72}{8}} = \sqrt{9} = 3$

11. $\sqrt{196} \div \sqrt{4} = \sqrt{\frac{196}{4}} = \sqrt{49} = 7$

12. $\sqrt{90} \div \sqrt{10} = \sqrt{\frac{90}{10}} = \sqrt{9} = 3$

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Right Column:

13. $\sqrt{15} \div \sqrt{375} = \sqrt{\frac{15}{375}} = \sqrt{\frac{1}{25}} = \frac{1}{5}$

14. $\sqrt{99} \div \sqrt{11} = \sqrt{\frac{99}{11}} = \sqrt{9} = 3$

15. $\sqrt{245} \div \sqrt{5} = \sqrt{\frac{245}{5}} = \sqrt{49} = 7$

16. $\sqrt{13} \div \sqrt{52} = \sqrt{\frac{13}{52}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$

17. $\sqrt{15} \div \sqrt{60} = \sqrt{\frac{15}{60}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$

18. $\sqrt{432} \div \sqrt{3} = \sqrt{\frac{432}{3}} = \sqrt{144} = 12$

19. $\sqrt{640} \div \sqrt{40} = \sqrt{\frac{640}{40}} = \sqrt{16} = 4$

20. $\sqrt{50} \div \sqrt{200} = \sqrt{\frac{50}{200}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$

21. $\sqrt{128} \div \sqrt{8} = \sqrt{\frac{128}{8}} = \sqrt{16} = 4$

22. $\sqrt{288} \div \sqrt{32} = \sqrt{\frac{288}{32}} = \sqrt{9} = 3$

23. $\sqrt{200} \div \sqrt{8} = \sqrt{\frac{200}{8}} = \sqrt{25} = 5$

24. $\sqrt{8} \div \sqrt{32} = \sqrt{\frac{8}{32}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$

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✔ Final Answers (in order):

Left Column:
1. $5$
2. $2$
3. $\frac{1}{2}$
4. $2$
5. $6$
6. $4$
7. $6$
8. $5$
9. $\frac{1}{4}$
10. $3$
11. $7$
12. $3$

Right Column:
13. $\frac{1}{5}$
14. $3$
15. $7$
16. $\frac{1}{2}$
17. $\frac{1}{2}$
18. $12$
19. $4$
20. $\frac{1}{2}$
21. $4$
22. $3$
23. $5$
24. $\frac{1}{2}$

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✔ Summary:

All answers are simplified radicals or rational numbers. The pattern is consistent: divide the numbers inside the square roots first, then simplify the resulting square root.

Let me know if you'd like this in a printable format!