Let’s solve each square root fraction step by step. We’ll simplify the fraction inside the square root first, then take the square root of the numerator and denominator separately if possible.
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1. √(10/40)
Simplify 10/40 = 1/4
√(1/4) = √1 / √4 = 1/2
2. √(11/99)
Simplify 11/99 = 1/9
√(1/9) = 1/3
3. √(25/49)
Both are perfect squares:
√25 = 5, √49 = 7 → 5/7
4. √(10/640)
Simplify 10/640 = 1/64
√(1/64) = 1/8
5. √(200/128)
Simplify: divide numerator and denominator by 8 → 25/16
√(25/16) = 5/4
6. √(324/441)
Check: 324 = 18², 441 = 21² → 18/21 = 6/7 (simplified)
Wait — let’s double-check:
Actually, 324 ÷ 9 = 36, 441 ÷ 9 = 49 → so √(36/49) = 6/7 ✔️
7. √(225/400)
225 = 15², 400 = 20² → 15/20 = 3/4
8. √(100/64)
100 = 10², 64 = 8² → 10/8 = 5/4
9. √(192/27)
Simplify: divide numerator and denominator by 3 → 64/9
√(64/9) = 8/3
10. √(18/32)
Simplify: divide by 2 → 9/16
√(9/16) = 3/4
11. √(20/80)
Simplify: 20/80 = 1/4 → √(1/4) = 1/2
12. √(4/64)
4/64 = 1/16 → √(1/16) = 1/4
13. √(54/96)
Simplify: divide by 6 → 9/16 → √(9/16) = 3/4
Wait — check: 54 ÷ 6 = 9, 96 ÷ 6 = 16 → yes → 3/4 ✔️
14. √(27/75)
Divide by 3 → 9/25 → √(9/25) = 3/5
15. √(10/90)
10/90 = 1/9 → √(1/9) = 1/3
16. √(20/125)
Divide by 5 → 4/25 → √(4/25) = 2/5
17. √(200/800)
200/800 = 1/4 → √(1/4) = 1/2
18. √(110/990)
Divide by 110 → 1/9 → √(1/9) = 1/3
19. √(125/500)
125/500 = 1/4 → √(1/4) = 1/2
20. √(10/250)
10/250 = 1/25 → √(1/25) = 1/5
21. √(100/625)
100 = 10², 625 = 25² → 10/25 = 2/5
22. √(12/48)
12/48 = 1/4 → √(1/4) = 1/2
23. √(2/72)
2/72 = 1/36 → √(1/36) = 1/6
24. √(3/75)
3/75 = 1/25 → √(1/25) = 1/5
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Final Answer:
1. 1/2
2. 1/3
3. 5/7
4. 1/8
5. 5/4
6. 6/7
7. 3/4
8. 5/4
9. 8/3
10. 3/4
11. 1/2
12. 1/4
13. 3/4
14. 3/5
15. 1/3
16. 2/5
17. 1/2
18. 1/3
19. 1/2
20. 1/5
21. 2/5
22. 1/2
23. 1/6
24. 1/5
Parent Tip: Review the logic above to help your child master the concept of square root worksheet.
