Here is the completed
Square Roots Worksheet with all answers rounded to
3 decimal places, as requested.
---
✔ Solutions:
| Problem | Square Root | Rounded to 3 Decimals |
|---------|-------------|------------------------|
|
1 a. √217 | ≈ 14.7308... |
14.731 |
|
1 b. √84 | ≈ 9.1651... |
9.165 |
|
2 a. √55 | ≈ 7.4161... |
7.416 |
|
2 b. √111 | ≈ 10.5356... |
10.536 |
|
3 a. √163 | ≈ 12.7671... |
12.767 |
|
3 b. √52 | ≈ 7.2111... |
7.211 |
|
4 a. √146 | ≈ 12.0830... |
12.083 |
|
4 b. √274 | ≈ 16.5529... |
16.553 |
|
5 a. √102 | ≈ 10.0995... |
10.100 |
|
5 b. √91 | ≈ 9.5393... |
9.539 |
|
6 a. √188 | ≈ 13.7113... |
13.711 |
|
6 b. √130 | ≈ 11.4017... |
11.402 |
|
7 a. √65 | ≈ 8.0622... |
8.062 |
|
7 b. √110 | ≈ 10.4880... |
10.488 |
|
8 a. √7 | ≈ 2.6457... |
2.646 |
|
8 b. √176 | ≈ 13.2664... |
13.266 |
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📝 Explanation of How to Solve:
To find the square root of a number (like √217), you are looking for a number that, when multiplied by itself, equals the original number.
Since most of these numbers are
not perfect squares, their square roots are
irrational numbers — meaning they have non-repeating, non-terminating decimals. So we use a calculator (or estimation methods) to approximate them.
#### 🔢 Rounding to 3 Decimal Places:
- Look at the
fourth decimal digit.
- If it’s
5 or greater, round up the third digit.
- If it’s
less than 5, leave the third digit unchanged.
✔ Example:
√217 ≈ 14.7308 → Fourth digit is
8 → Round up →
14.731
---
💡 Tip for Students:
You can check your work by squaring your answer. For example:
> 14.731² = 14.731 × 14.731 ≈ 217.00 (close enough!)
This helps verify your rounding was correct.
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Let me know if you’d like a printable version or step-by-step manual calculation methods (like long division for square roots)!
Parent Tip: Review the logic above to help your child master the concept of exponents and roots worksheet.
