Absolutely! Let’s solve each problem step by step, explaining the reasoning behind each solution. The worksheet focuses on
square roots combined with exponents, addition, subtraction, multiplication, division, and perfect squares.
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🔢 Problem 1:
> √(2 × 8) − √16
- First, simplify inside the square root:
2 × 8 = 16 → √16 = 4
√16 = 4 (again)
- So: 4 − 4 =
0
✔ Answer: 0
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🔢 Problem 2:
> √324 / √25
- √324 = 18 (since 18² = 324)
- √25 = 5
- So: 18 ÷ 5 =
3.6 or
18/5
✔ Answer: 18/5 or 3.6
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🔢 Problem 3:
> √324 / √36
- √324 = 18
- √36 = 6
- 18 ÷ 6 =
3
✔ Answer: 3
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🔢 Problem 4:
> √(20 × 20) − √289
- √(20 × 20) = √400 = 20
- √289 = 17 (since 17² = 289)
- 20 − 17 =
3
✔ Answer: 3
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🔢 Problem 5:
> √441 + √(183²)
- √441 = 21 (since 21² = 441)
- √(183²) = 183 (square root of a square is the absolute value — here, positive)
- 21 + 183 =
204
✔ Answer: 204
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🔢 Problem 6:
> (√(80 + 1))²
- Inside: 80 + 1 = 81 → √81 = 9
- Then square it: 9² =
81
✔ Answer: 81
*(Note: (√x)² = x, as long as x ≥ 0)*
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🔢 Problem 7:
> √(128/8) + √16
- 128 ÷ 8 = 16 → √16 = 4
- √16 = 4
- 4 + 4 =
8
✔ Answer: 8
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🔢 Problem 8:
> (√(144/4))²
- 144 ÷ 4 = 36 → √36 = 6
- 6² =
36
✔ Answer: 36
*(Again, (√x)² = x)*
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🔢 Problem 9:
> √(300 + 24) / √(80 + 1)
- Numerator: 300 + 24 = 324 → √324 = 18
- Denominator: 80 + 1 = 81 → √81 = 9
- 18 ÷ 9 =
2
✔ Answer: 2
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🔢 Problem 10:
> √(1200/3) + √81
- 1200 ÷ 3 = 400 → √400 = 20
- √81 = 9
- 20 + 9 =
29
✔ Answer: 29
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🔢 Problem 11:
> (√(7 × 7))²
- 7 × 7 = 49 → √49 = 7
- 7² =
49
✔ Answer: 49
*(Same as Problem 6 & 8 — (√x)² = x)*
---
🔢 Problem 12:
> √(166²) + √36
- √(166²) = 166
- √36 = 6
- 166 + 6 =
172
✔ Answer: 172
---
🔢 Problem 13:
> (√(53 + 28))²
- 53 + 28 = 81 → √81 = 9
- 9² =
81
✔ Answer: 81
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🔢 Problem 14:
> √(14 × 14) / √49
- √(14×14) = 14
- √49 = 7
- 14 ÷ 7 =
2
✔ Answer: 2
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🔢 Problem 15:
> √36 / √(3 × 3)
- √36 = 6
- 3 × 3 = 9 → √9 = 3
- 6 ÷ 3 =
2
✔ Answer: 2
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🔢 Problem 16:
> √169 + √(51 + 13)
- √169 = 13
- 51 + 13 = 64 → √64 = 8
- 13 + 8 =
21
✔ Answer: 21
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🔢 Problem 17:
> √361 + √(106 − 25)
- √361 = 19 (since 19² = 361)
- 106 − 25 = 81 → √81 = 9
- 19 + 9 =
28
✔ Answer: 28
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🔢 Problem 18:
> √9 × √(3 × 3)
- √9 = 3
- 3 × 3 = 9 → √9 = 3
- 3 × 3 =
9
✔ Answer: 9
*(You could also combine under one root: √(9 × 9) = √81 = 9)*
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🔢 Problem 19:
> √324 − √(198 + 58)
- √324 = 18
- 198 + 58 = 256 → √256 = 16
- 18 − 16 =
2
✔ Answer: 2
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🔢 Problem 20:
> √(155²)
- Square root of a square: √(155²) =
155
✔ Answer: 155
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##
✔ Final Answers Summary:
1.
0
2.
18/5 or 3.6
3.
3
4.
3
5.
204
6.
81
7.
8
8.
36
9.
2
10.
29
11.
49
12.
172
13.
81
14.
2
15.
2
16.
21
17.
28
18.
9
19.
2
20.
155
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Let me know if you’d like these explained in more detail or turned into a printable answer key! 😊
Parent Tip: Review the logic above to help your child master the concept of dividing square roots worksheet.
