Let's solve each problem on the
Square Roots Worksheet step by step.
---
1 a. √91 + 9
- √91 is not a perfect square.
- √81 = 9, √100 = 10 → √91 ≈ 9.54 (approximately)
- So: √91 + 9 ≈ 9.54 + 9 =
18.54
✔ Answer: ≈
18.54 (or leave as √91 + 9 if exact form is needed)
---
1 b. √47 + 2
- √47 is not a perfect square.
- √36 = 6, √49 = 7 → √47 ≈ 6.86
- So: √47 + 2 ≈ 6.86 + 2 =
8.86
✔ Answer: ≈
8.86
---
2 a. √4 + √100
- √4 = 2
- √100 = 10
- 2 + 10 =
12
✔ Answer: 12
---
2 b. √19 + 125
- √19 is not a perfect square.
- √16 = 4, √25 = 5 → √19 ≈ 4.36
- So: √19 + 125 ≈ 4.36 + 125 =
129.36
✔ Answer: ≈
129.36
---
3 a. √9 + 0
- √9 = 3
- 3 + 0 =
3
✔ Answer: 3
---
3 b. √36 + √49
- √36 = 6
- √49 = 7
- 6 + 7 =
13
✔ Answer: 13
---
4 a. √49 – √144
- √49 = 7
- √144 = 12
- 7 – 12 =
–5
✔ Answer: –5
---
4 b. √9 + √25
- √9 = 3
- √25 = 5
- 3 + 5 =
8
✔ Answer: 8
---
5 a. √121 + √49
- √121 = 11
- √49 = 7
- 11 + 7 =
18
✔ Answer: 18
---
5 b. √35 – 26
- √35 is not a perfect square.
- √25 = 5, √36 = 6 → √35 ≈ 5.92
- So: √35 – 26 ≈ 5.92 – 26 =
–20.08
✔ Answer: ≈
–20.08
---
6 a. √9 – √9
- √9 = 3
- 3 – 3 =
0
✔ Answer: 0
---
6 b. √245 – 101
- √245:
- 15² = 225, 16² = 256 → √245 ≈ 15.65
- So: √245 – 101 ≈ 15.65 – 101 =
–85.35
✔ Answer: ≈
–85.35
---
7 a. √4 – √121
- √4 = 2
- √121 = 11
- 2 – 11 =
–9
✔ Answer: –9
---
7 b. √33 + 3
- √33 is not a perfect square.
- √25 = 5, √36 = 6 → √33 ≈ 5.74
- So: √33 + 3 ≈ 5.74 + 3 =
8.74
✔ Answer: ≈
8.74
---
✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1a | √91 + 9 ≈
18.54 |
| 1b | √47 + 2 ≈
8.86 |
| 2a |
12 |
| 2b | √19 + 125 ≈
129.36 |
| 3a |
3 |
| 3b |
13 |
| 4a |
–5 |
| 4b |
8 |
| 5a |
18 |
| 5b | √35 – 26 ≈
–20.08 |
| 6a |
0 |
| 6b | √245 – 101 ≈
–85.35 |
| 7a |
–9 |
| 7b | √33 + 3 ≈
8.74 |
> 💡
Note: For problems involving non-perfect squares (like √91, √47), answers are approximate unless left in radical form. Since the worksheet asks to "solve," decimal approximations are acceptable for real-world understanding.
Let me know if you'd like the exact forms or more explanation!
Parent Tip: Review the logic above to help your child master the concept of perfect square roots worksheet.
