Let’s solve each problem step by step. We’ll find square roots, simplify expressions, and use basic math rules.
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1. √(0/8)
0 divided by 8 is 0.
√0 = 0
→
Answer: 0
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2. √361 – √121
√361 = 19 (because 19×19=361)
√121 = 11 (because 11×11=121)
19 – 11 = 8
→
Answer: 8
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3. √144 + √169
√144 = 12
√169 = 13
12 + 13 = 25
→
Answer: 25
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4. √(3 × 27)
3 × 27 = 81
√81 = 9
→
Answer: 9
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5. √196 – √36
√196 = 14
√36 = 6
14 – 6 = 8
→
Answer: 8
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6. √289 + √9
√289 = 17
√9 = 3
17 + 3 = 20
→
Answer: 20
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7. √(22 + 42)
22 + 42 = 64
√64 = 8
→
Answer: 8
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8. √(3 + 6)
3 + 6 = 9
√9 = 3
→
Answer: 3
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9. √256 / √16
√256 = 16
√16 = 4
16 ÷ 4 = 4
→
Answer: 4
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10. √(2888 / 8)
First, divide: 2888 ÷ 8 = 361
Then √361 = 19
→
Answer: 19
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11. √(441 / 9)
441 ÷ 9 = 49
√49 = 7
→
Answer: 7
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12. √(63 × 7)
63 × 7 = 441
√441 = 21
→
Answer: 21
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13. (√144)²
√144 = 12
12² = 144
Or remember: squaring a square root cancels it → just get the number inside!
→
Answer: 144
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14. √(8 + 41)
8 + 41 = 49
√49 = 7
→
Answer: 7
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15. √(2 × 8)
2 × 8 = 16
√16 = 4
→
Answer: 4
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16. √(113²)
Square root of a square = the original number (if positive)
So √(113²) = 113
→
Answer: 113
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17. √(1372 / 7)
1372 ÷ 7 = 196
√196 = 14
→
Answer: 14
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18. √(81 × 4)
81 × 4 = 324
√324 = 18
*(Hint: You can also do √81 × √4 = 9 × 2 = 18)*
→
Answer: 18
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19. √49 + √169
√49 = 7
√169 = 13
7 + 13 = 20
→
Answer: 20
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20. √(5 × 5)
5 × 5 = 25
√25 = 5
→
Answer: 5
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Final Answer:
1. 0
2. 8
3. 25
4. 9
5. 8
6. 20
7. 8
8. 3
9. 4
10. 19
11. 7
12. 21
13. 144
14. 7
15. 4
16. 113
17. 14
18. 18
19. 20
20. 5
Parent Tip: Review the logic above to help your child master the concept of operations with roots worksheet.
