Perfect Squares and Square Roots Notes - Free Printable

It looks like you've uploaded a worksheet titled "Perfect Squares & Square Roots". The goal of this worksheet is to help students understand and practice perfect squares and square roots.

Let me solve the problems on the worksheet step by step and explain the concepts.

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🔹 Part 1: Perfect Squares

This section asks for the square of numbers from 1² to 12².

We calculate each:

| Number | Square |
|--------|--------|
| 1² = | 1 |
| 2² = | 4 |
| 3² = | 9 |
| 4² = | 16 |
| 5² = | 25 |
| 6² = | 36 |
| 7² = | 49 |
| 8² = | 64 |
| 9² = | 81 |
| 10² = | 100 |
| 11² = | 121 |
| 12² = | 144 |

✔ So, fill in:
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
- 6² = 36
- 7² = 49
- 8² = 64
- 9² = 81
- 10² = 100
- 11² = 121
- 12² = 144

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🔹 Part 2: Square Roots

This section asks for the square root of various perfect squares.

We are looking for the number that, when multiplied by itself, gives the number under the square root.

Let’s go through them:

| Square Root | Answer | Explanation |
|-------------|--------|-----------|
| √1 = | 1 | Because 1 × 1 = 1 |
| √4 = | 2 | Because 2 × 2 = 4 |
| √9 = | 3 | Because 3 × 3 = 9 |
| √16 = | 4 | Because 4 × 4 = 16 |
| √25 = | 5 | Because 5 × 5 = 25 |
| √36 = | 6 | Because 6 × 6 = 36 |
| √49 = | 7 | Because 7 × 7 = 49 |
| √64 = | 8 | Because 8 × 8 = 64 |
| √81 = | 9 | Because 9 × 9 = 81 |
| √100 = | 10 | Because 10 × 10 = 100 |
| √121 = | 11 | Because 11 × 11 = 121 |
| √144 = | 12 | Because 12 × 12 = 144 |
| √169 = | 13 | Because 13 × 13 = 169 |
| √196 = | 14 | Because 14 × 14 = 196 |
| √225 = | 15 | Because 15 × 15 = 225 |
| √256 = | 16 | Because 16 × 16 = 256 |
| √289 = | 17 | Because 17 × 17 = 289 |
| √324 = | 18 | Because 18 × 18 = 324 |
| √361 = | 19 | Because 19 × 19 = 361 |
| √400 = | 20 | Because 20 × 20 = 400 |

✔ So, fill in:
- √1 = 1
- √4 = 2
- √9 = 3
- √16 = 4
- √25 = 5
- √36 = 6
- √49 = 7
- √64 = 8
- √81 = 9
- √100 = 10
- √121 = 11
- √144 = 12
- √169 = 13
- √196 = 14
- √225 = 15
- √256 = 16
- √289 = 17
- √324 = 18
- √361 = 19
- √400 = 20

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🔹 Definitions (as shown in the worksheet)

> The result of a number multiplied by itself:
> Example: 4 × 4 = 4² = 16 → This is called a perfect square.

> The number multiplied by itself to produce a new number (of squaring):
> Example: √16 = 4 → This is called the square root.

So:
- Squaring means multiplying a number by itself.
- Square root is the reverse — finding what number was squared to get the result.

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✔ Final Answers Summary

#### Perfect Squares:
```
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144
```

#### Square Roots:
```
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12
√169 = 13
√196 = 14
√225 = 15
√256 = 16
√289 = 17
√324 = 18
√361 = 19
√400 = 20
```

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Let me know if you'd like this as a printable PDF or need help with non-perfect square roots too!