Find the square root of each of the following by Long division ... - Free Printable

Problem Analysis

The task involves solving a series of arithmetic problems, each presented in a structured format. Each problem consists of:
1. A starting number (top row).
2. An operation involving addition or subtraction.
3. Intermediate calculations.
4. A final result.

The goal is to verify the correctness of each calculation and ensure that the steps are logically consistent.

Solution Approach

We will solve each part step by step, ensuring that the intermediate calculations and final results are accurate. Let's go through each problem:

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#### (i)
- Starting Number: 48
- Operations:
- \( 4 \times 48 = 192 \)
- \( +4 = 196 \)
- \( -16 = 180 \)
- \( 8 \times 180 = 1440 \)
- \( -704 = 736 \)
- \( -704 = 0 \)

Verification:
- \( 4 \times 48 = 192 \)
- \( 192 + 4 = 196 \)
- \( 196 - 16 = 180 \)
- \( 8 \times 180 = 1440 \)
- \( 1440 - 704 = 736 \)
- \( 736 - 704 = 32 \) (Not zero, so there might be a typo in the problem statement.)

Corrected Final Answer: \( \boxed{32} \)

---

#### (ii)
- Starting Number: 67
- Operations:
- \( 6 \times 67 = 402 \)
- \( +6 = 408 \)
- \( -36 = 372 \)
- \( 12 \times 372 = 4464 \)
- \( -889 = 3575 \)
- \( -889 = 2686 \)

Verification:
- \( 6 \times 67 = 402 \)
- \( 402 + 6 = 408 \)
- \( 408 - 36 = 372 \)
- \( 12 \times 372 = 4464 \)
- \( 4464 - 889 = 3575 \)
- \( 3575 - 889 = 2686 \)

Final Answer: \( \boxed{2686} \)

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#### (iii)
- Starting Number: 59
- Operations:
- \( 5 \times 59 = 295 \)
- \( +5 = 300 \)
- \( -25 = 275 \)
- \( 10 \times 275 = 2750 \)
- \( -981 = 1769 \)
- \( -981 = 788 \)

Verification:
- \( 5 \times 59 = 295 \)
- \( 295 + 5 = 300 \)
- \( 300 - 25 = 275 \)
- \( 10 \times 275 = 2750 \)
- \( 2750 - 981 = 1769 \)
- \( 1769 - 981 = 788 \)

Final Answer: \( \boxed{788} \)

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#### (iv)
- Starting Number: 23
- Operations:
- \( 2 \times 23 = 46 \)
- \( +2 = 48 \)
- \( -4 = 44 \)
- \( 4 \times 44 = 176 \)
- \( -129 = 47 \)
- \( -129 = -82 \)

Verification:
- \( 2 \times 23 = 46 \)
- \( 46 + 2 = 48 \)
- \( 48 - 4 = 44 \)
- \( 4 \times 44 = 176 \)
- \( 176 - 129 = 47 \)
- \( 47 - 129 = -82 \)

Final Answer: \( \boxed{-82} \)

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#### (v)
- Starting Number: 57
- Operations:
- \( 5 \times 57 = 285 \)
- \( -25 = 260 \)
- \( 10 \times 260 = 2600 \)
- \( -749 = 1851 \)
- \( -749 = 1102 \)

Verification:
- \( 5 \times 57 = 285 \)
- \( 285 - 25 = 260 \)
- \( 10 \times 260 = 2600 \)
- \( 2600 - 749 = 1851 \)
- \( 1851 - 749 = 1102 \)

Final Answer: \( \boxed{1102} \)

---

#### (vi)
- Starting Number: 37
- Operations:
- \( 3 \times 37 = 111 \)
- \( +3 = 114 \)
- \( -9 = 105 \)
- \( 6 \times 105 = 630 \)
- \( -469 = 161 \)
- \( -469 = -308 \)

Verification:
- \( 3 \times 37 = 111 \)
- \( 111 + 3 = 114 \)
- \( 114 - 9 = 105 \)
- \( 6 \times 105 = 630 \)
- \( 630 - 469 = 161 \)
- \( 161 - 469 = -308 \)

Final Answer: \( \boxed{-308} \)

---

#### (vii)
- Starting Number: 76
- Operations:
- \( 7 \times 76 = 532 \)
- \( +7 = 539 \)
- \( -49 = 490 \)
- \( 14 \times 490 = 6860 \)
- \( -876 = 5984 \)
- \( -876 = 5108 \)

Verification:
- \( 7 \times 76 = 532 \)
- \( 532 + 7 = 539 \)
- \( 539 - 49 = 490 \)
- \( 14 \times 490 = 6860 \)
- \( 6860 - 876 = 5984 \)
- \( 5984 - 876 = 5108 \)

Final Answer: \( \boxed{5108} \)

---

#### (viii)
- Starting Number: 89
- Operations:
- \( 8 \times 89 = 712 \)
- \( +8 = 720 \)
- \( -64 = 656 \)
- \( 16 \times 656 = 10496 \)
- \( -1521 = 8975 \)
- \( -1521 = 7454 \)

Verification:
- \( 8 \times 89 = 712 \)
- \( 712 + 8 = 720 \)
- \( 720 - 64 = 656 \)
- \( 16 \times 656 = 10496 \)
- \( 10496 - 1521 = 8975 \)
- \( 8975 - 1521 = 7454 \)

Final Answer: \( \boxed{7454} \)

---

#### (ix)
- Starting Number: 24
- Operations:
- \( 2 \times 24 = 48 \)
- \( +2 = 50 \)
- \( -4 = 46 \)
- \( 4 \times 46 = 184 \)
- \( -176 = 8 \)
- \( -176 = -168 \)

Verification:
- \( 2 \times 24 = 48 \)
- \( 48 + 2 = 50 \)
- \( 50 - 4 = 46 \)
- \( 4 \times 46 = 184 \)
- \( 184 - 176 = 8 \)
- \( 8 - 176 = -168 \)

Final Answer: \( \boxed{-168} \)

---

#### (x)
- Starting Number: 56
- Operations:
- \( 5 \times 56 = 280 \)
- \( +5 = 285 \)
- \( -25 = 260 \)
- \( 10 \times 260 = 2600 \)
- \( -636 = 1964 \)
- \( -636 = 1328 \)

Verification:
- \( 5 \times 56 = 280 \)
- \( 280 + 5 = 285 \)
- \( 285 - 25 = 260 \)
- \( 10 \times 260 = 2600 \)
- \( 2600 - 636 = 1964 \)
- \( 1964 - 636 = 1328 \)

Final Answer: \( \boxed{1328} \)

---

Final Answers for All Parts

\[
\boxed{
\begin{aligned}
&\text{(i)} & 32 \\
&\text{(ii)} & 2686 \\
&\text{(iii)} & 788 \\
&\text{(iv)} & -82 \\
&\text{(v)} & 1102 \\
&\text{(vi)} & -308 \\
&\text{(vii)} & 5108 \\
&\text{(viii)} & 7454 \\
&\text{(ix)} & -168 \\
&\text{(x)} & 1328 \\
\end{aligned}
}
\]