Concept-HW-G8- Finding Square Roots Using Long Division worksheet ... - Free Printable

Let's solve each of the given numbers using the long division method to find their square roots. The long division method is a step-by-step process used to find the square root of a number, especially useful for non-perfect squares or when you want to avoid calculators.

We'll go through each number one by one.

---

🔷 1. √4225

#### Step 1: Group digits in pairs from right to left
```
42 | 25
```

#### Step 2: Find the largest number whose square ≤ 42
- 6² = 36 ≤ 42
- 7² = 49 > 42 → So, use 6

Write 6 as the first digit of the quotient.

```
6
----
6 | 42
-36
----
6
```

Bring down the next pair (25), so we have 625.

#### Step 3: Double the current quotient (6) → 12
Now find a digit x such that:
> (12x) × x ≤ 625

Try:
- 125 × 5 = 625 → Perfect!

So, second digit is 5

```
65
------
6 | 42 25
-36
----
6 25
-6 25
-------
0
```

✔ So, √4225 = 65

---

🔷 2. √5476

Group:
```
54 | 76
```

#### Step 1: Largest number whose square ≤ 54
- 7² = 49 ≤ 54
- 8² = 64 > 54 → Use 7

Quotient so far: 7

```
7
----
7 | 54
-49
----
5
```

Bring down 76 → 576

Double the quotient: 7 × 2 = 14

Find digit x such that (14x) × x ≤ 576

Try:
- 144 × 4 = 576 → Yes!

So, second digit is 4

```
74
------
7 | 54 76
-49
----
5 76
-5 76
-------
0
```

✔ So, √5476 = 74

---

🔷 3. √3481

Group:
```
34 | 81
```

Largest number whose square ≤ 34:
- 5² = 25
- 6² = 36 > 34 → Use 5

Quotient: 5

```
5
----
5 | 34
-25
----
9
```

Bring down 81 → 981

Double quotient: 5 × 2 = 10

Find digit x such that (10x) × x ≤ 981

Try:
- 107 × 7 = 749 → too small
- 108 × 8 = 864
- 109 × 9 = 981 → YES!

So, second digit is 9

```
59
------
5 | 34 81
-25
----
9 81
-9 81
-------
0
```

✔ So, √3481 = 59

---

🔷 4. √2304

Group:
```
23 | 04
```

Largest number whose square ≤ 23:
- 4² = 16
- 5² = 25 > 23 → Use 4

Quotient: 4

```
4
----
4 | 23
-16
----
7
```

Bring down 04 → 704

Double quotient: 4 × 2 = 8

Find digit x such that (8x) × x ≤ 704

Try:
- 88 × 8 = 704 → YES!

So, second digit is 8

```
48
------
4 | 23 04
-16
----
7 04
-7 04
-------
0
```

✔ So, √2304 = 48

---

🔷 5. √5329

Group:
```
53 | 29
```

Largest number whose square ≤ 53:
- 7² = 49
- 8² = 64 > 53 → Use 7

Quotient: 7

```
7
----
7 | 53
-49
----
4
```

Bring down 29 → 429

Double quotient: 7 × 2 = 14

Find digit x such that (14x) × x ≤ 429

Try:
- 143 × 3 = 429 → YES!

So, second digit is 3

```
73
------
7 | 53 29
-49
----
4 29
-4 29
-------
0
```

✔ So, √5329 = 73

---

✔ Final Answers:

| Number | Square Root |
|--------|-------------|
| 1. 4225 | 65 |
| 2. 5476 | 74 |
| 3. 3481 | 59 |
| 4. 2304 | 48 |
| 5. 5329 | 73 |

All are perfect squares! 😊

Let me know if you'd like a visual diagram of any step!