Inverse Operations: Squares and Roots

Name: _______________________________
Date: _______________________________

Remember: Squaring and finding the square root are inverse operations. If 5² = 25, then √25 = 5.

Part A: Perfect Squares

Calculate the following:

1. 7² = __________
2. 12² = __________
3. 9² = __________
4. 15² = __________
5. 11² = __________
6. 20² = __________
7. 13² = __________
8. 6² = __________

Part B: Square Roots

Find the square root of each number:

9. √64 = __________
10. √100 = __________
11. √49 = __________
12. √144 = __________
13. √81 = __________
14. √169 = __________
15. √225 = __________
16. √196 = __________

Part C: Using the Inverse Relationship

Fill in the missing values:

17. If 8² = 64, then √64 = __________
18. If √121 = 11, then 11² = __________
19. If 14² = 196, then √196 = __________
20. If √400 = 20, then 20² = __________
21. If 16² = 256, then √256 = __________

Part D: Problem Solving

22. A square garden has an area of 289 m². What is the length of one side?

Answer: __________

23. If you square a number and get 361, what was the original number?

Answer: __________

24. What number, when multiplied by itself, equals 324?

Answer: __________