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 number results.
Let me know if you'd like exact forms or further explanation!
Parent Tip: Review the logic above to help your child master the concept of squares and square roots worksheet.
