Find the square roots of the following using division method

Options

A. 390625
B. 4489
C. 3249
D. 529

Answer

To find the square roots of the given numbers using the division method, we will follow a systematic approach. Let's go through the steps for each of the numbers provided in the video transcript.

### Step-by-Step Solution:

#### 1. Finding the Square Root of 390625

**Step 1:** Pair the digits from right to left.
- Pairs: (39)(06)(25)

**Step 2:** Find the largest square less than or equal to the first pair (39).
- The largest square is \(6^2 = 36\).
- Write down 6 as part of the root.

**Step 3:** Subtract and bring down the next pair.
- \(39 - 36 = 3\)
- Bring down 06 to make it 306.

**Step 4:** Double the current root (6) and find a digit (d) such that \( (12d) \times d \leq 306 \).
- Trying \(d = 2\): \(122 \times 2 = 244\) (valid)
- Trying \(d = 3\): \(123 \times 3 = 369\) (invalid)
- Write down 2.

**Step 5:** Subtract and bring down the next pair.
- \(306 - 244 = 62\)
- Bring down 25 to make it 6225.

**Step 6:** Double the current root (62) and find a digit (d) such that \( (124d) \times d \leq 6225 \).
- Trying \(d = 5\): \(1245 \times 5 = 6225\) (valid)
- Write down 5.

**Step 7:** Subtract to find the remainder.
- \(6225 - 6225 = 0\)

**Conclusion:** The square root of 390625 is **625**.

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#### 2. Finding the Square Root of 4489

**Step 1:** Pair the digits from right to left.
- Pairs: (44)(89)

**Step 2:** Find the largest square less than or equal to the first pair (44).
- The largest square is \(6^2 = 36\).
- Write down 6.

**Step 3:** Subtract and bring down the next pair.
- \(44 - 36 = 8\)
- Bring down 89 to make it 889.

**Step 4:** Double the current root (6) and find a digit (d) such that \( (12d) \times d \leq 889 \).
- Trying \(d = 7\): \(127 \times 7 = 889\) (valid)
- Write down 7.

**Step 5:** Subtract to find the remainder.
- \(889 - 889 = 0\)

**Conclusion:** The square root of 4489 is **67**.

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#### 3. Finding the Square Root of 3249

**Step 1:** Pair the digits from right to left.
- Pairs: (32)(49)

**Step 2:** Find the largest square less than or equal to the first pair (32).
- The largest square is \(5^2 = 25\).
- Write down 5.

**Step 3:** Subtract and bring down the next pair.
- \(32 - 25 = 7\)
- Bring down 49 to make it 749.

**Step 4:** Double the current root (5) and find a digit (d) such that \( (10d) \times d \leq 749 \).
- Trying \(d = 7\): \(107 \times 7 = 749\) (valid)
- Write down 7.

**Step 5:** Subtract to find the remainder.
- \(749 - 749 = 0\)

**Conclusion:** The square root of 3249 is **57**.

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#### 4. Finding the Square Root of 529

**Step 1:** Pair the digits from right to left.
- Pairs: (5)(29)

**Step 2:** Find the largest square less than or equal to the first pair (5).
- The largest square is \(2^2 = 4\).
- Write down 2.

**Step 3:** Subtract and bring down the next pair.
- \(5 - 4 = 1\)
- Bring down 29 to make it 129.

**Step 4:** Double the current root (2) and find a digit (d) such that \( (4d) \times d \leq 129 \).
- Trying \(d = 3\): \(43 \times 3 = 129\) (valid)
- Write down 3.

**Step 5:** Subtract to find the remainder.
- \(129 - 129 = 0\)

**Conclusion:** The square root of 529 is **23**.

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### Summary of Square Roots:
- Square root of 390625 is **625**.
- Square root of 4489 is **67**.
- Square root of 3249 is **57**.
- Square root of 529 is **23**.