Divide the following numbers by the given index radical: 1. [9]1009 2. [4]828 3. [13]525 4. [17]684 5. [41]1331 6. [23]713

Mathematics
Divide the following numbers by the given index radical: 1. [9]1009 2. [4]828 3. [13]525 4. [17]684 5. [41]1331 6. [23]713

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Answer

114 R 3

Here are the solutions to the division problems:

1. Divide 10291029 by 99 Step 1: Divide 1010 by 99.

19)1029‾−9↓1\begin{array}{r} 1 \\ 9 \overline{) 1029} \\ -9 \downarrow \\ \hline 1 \end{array}

Step 2: Bring down the next digit, 22. Divide 1212 by 99.

119)1029‾−9↓12−9↓3\begin{array}{r} 11 \\ 9 \overline{) 1029} \\ -9 \downarrow \\ \hline 12 \\ -9 \downarrow \\ \hline 3 \end{array}

Step 3: Bring down the next digit, 99. Divide 3939 by 99.

1149)1029‾−9↓12−9↓39−363\begin{array}{r} 114 \\ 9 \overline{) 1029} \\ -9 \downarrow \\ \hline 12 \\ -9 \downarrow \\ \hline 39 \\ -36 \\ \hline 3 \end{array}

The quotient is 114114 with a remainder of 33. So, 10299=114R3\frac{1029}{9} = 114 R 3.

Final Answer: 114R3\boxed{114 R 3}

2. Divide 828828 by 44 Step 1: Divide 88 by 44.

24)828‾−8↓0\begin{array}{r} 2 \\ 4 \overline{) 828} \\ -8 \downarrow \\ \hline 0 \end{array}

Step 2: Bring down the next digit, 22. Divide 22 by 44.

204)828‾−8↓02−0↓2\begin{array}{r} 20 \\ 4 \overline{) 828} \\ -8 \downarrow \\ \hline 02 \\ -0 \downarrow \\ \hline 2 \end{array}

Step 3: Bring down the next digit, 88. Divide 2828 by 44.

2074)828‾−8↓02−0↓28−280\begin{array}{r} 207 \\ 4 \overline{) 828} \\ -8 \downarrow \\ \hline 02 \\ -0 \downarrow \\ \hline 28 \\ -28 \\ \hline 0 \end{array}

The quotient is 207207 with a remainder of 00. So, 8284=207\frac{828}{4} = 207.

Final Answer: 207\boxed{207}

3. Divide 585585 by 1313 Step 1: Divide 5858 by 1313. (13×4=5213 \times 4 = 52)

413)585‾−52↓6\begin{array}{r} 4 \\ 13 \overline{) 585} \\ -52 \downarrow \\ \hline 6 \end{array}

Step 2: Bring down the next digit, 55. Divide 6565 by 1313. (13×5=6513 \times 5 = 65)

4513)585‾−52↓65−650\begin{array}{r} 45 \\ 13 \overline{) 585} \\ -52 \downarrow \\ \hline 65 \\ -65 \\ \hline 0 \end{array}

The quotient is 4545 with a remainder of 00. So, 58513=45\frac{585}{13} = 45.

Final Answer: 45\boxed{45}

4. Divide 684684 by 1717 Step 1: Divide 6868 by 1717. (17×4=6817 \times 4 = 68)

417)684‾−68↓0\begin{array}{r} 4 \\ 17 \overline{) 684} \\ -68 \downarrow \\ \hline 0 \end{array}

Step 2: Bring down the next digit, 44. Divide 44 by 1717.

4017)684‾−68↓04−04\begin{array}{r} 40 \\ 17 \overline{) 684} \\ -68 \downarrow \\ \hline 04 \\ -0 \\ \hline 4 \end{array}

The quotient is 4040 with a remainder of 44. So, 68417=40R4\frac{684}{17} = 40 R 4.

Final Answer: 40R4\boxed{40 R 4}

5. Divide 18811881 by 4141 Step 1: Divide 188188 by 4141. (41×4=16441 \times 4 = 164)

441)1881‾−164↓24\begin{array}{r} 4 \\ 41 \overline{) 1881} \\ -164 \downarrow \\ \hline 24 \end{array}

Step 2: Bring down the next digit, 11. Divide 241241 by 4141. (41×5=20541 \times 5 = 205, 41×6=24641 \times 6 = 246)

4541)1881‾−164↓241−20536\begin{array}{r} 45 \\ 41 \overline{) 1881} \\ -164 \downarrow \\ \hline 241 \\ -205 \\ \hline 36 \end{array}

The quotient is 4545 with a remainder of 3636. So, 188141=45R36\frac{1881}{41} = 45 R 36.

Final Answer: 45R36\boxed{45 R 36}

6. Divide 713713 by 2323 Step 1: Divide 7171 by 2323. (23×3=6923 \times 3 = 69)

323)713‾−69↓2\begin{array}{r} 3 \\ 23 \overline{) 713} \\ -69 \downarrow \\ \hline 2 \end{array}

Step 2: Bring down the next digit, 33. Divide 2323 by 2323. (23×1=2323 \times 1 = 23)

3123)713‾−69↓23−230\begin{array}{r} 31 \\ 23 \overline{) 713} \\ -69 \downarrow \\ \hline 23 \\ -23 \\ \hline 0 \end{array}

The quotient is 3131 with a remainder of 00. So, 71323=31\frac{713}{23} = 31.

Final Answer: 31\boxed{31}

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Quick Answer

1. Divide 1029 by 9 Step 1: Divide 10 by 9.

Divide the following numbers by the given index radical: 1. [9]1009 2. [4]828 3. [13]525 4. [17]684 5. [41]1331 6. [23]713
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Here are the solutions to the division problems: 1. Divide 1029 by 9 Step 1: Divide 10 by 9. r 1 \\ 9 ) 1029 \\ -9 \\ 1 Step 2: Bring down the next digit, 2. Divide 12 by 9. r 11 \\ 9 ) 1029 \\ -9 \\ 12 \\ -9 \\ 3 Step 3: Bring down the next digit, 9. Divide 39 by 9. r 114 \\ 9 ) 1029 \\ -9 \\ 12 \\ -9 \\ 39 \\ -36 \\ 3 The quotient is 114 with a remainder of 3. So, (1029)/(9) = 114 R 3. Final Answer: 114 R 3 2. Divide 828 by 4 Step 1: Divide 8 by 4. r 2 \\ 4 ) 828 \\ -8 \\ 0 Step 2: Bring down the next digit, 2. Divide 2 by 4. r 20 \\ 4 ) 828 \\ -8 \\ 02 \\ -0 \\ 2 Step 3: Bring down the next digit, 8. Divide 28 by 4. r 207 \\ 4 ) 828 \\ -8 \\ 02 \\ -0 \\ 28 \\ -28 \\ 0 The quotient is 207 with a remainder of 0. So, (828)/(4) = 207. Final Answer: 207 3. Divide 585 by 13 Step 1: Divide 58 by 13. (13 × 4 = 52) r 4 \\ 13 ) 585 \\ -52 \\ 6 Step 2: Bring down the next digit, 5. Divide 65 by 13. (13 × 5 = 65) r 45 \\ 13 ) 585 \\ -52 \\ 65 \\ -65 \\ 0 The quotient is 45 with a remainder of 0. So, (585)/(13) = 45. Final Answer: 45 4. Divide 684 by 17 Step 1: Divide 68 by 17. (17 × 4 = 68) r 4 \\ 17 ) 684 \\ -68 \\ 0 Step 2: Bring down the next digit, 4. Divide 4 by 17. r 40 \\ 17 ) 684 \\ -68 \\ 04 \\ -0 \\ 4 The quotient is 40 with a remainder of 4. So, (684)/(17) = 40 R 4. Final Answer: 40 R 4 5. Divide 1881 by 41 Step 1: Divide 188 by 41. (41 × 4 = 164) r 4 \\ 41 ) 1881 \\ -164 \\ 24 Step 2: Bring down the next digit, 1. Divide 241 by 41. (41 × 5 = 205, 41 × 6 = 246) r 45 \\ 41 ) 1881 \\ -164 \\ 241 \\ -205 \\ 36 The quotient is 45 with a remainder of 36. So, (1881)/(41) = 45 R 36. Final Answer: 45 R 36 6. Divide 713 by 23 Step 1: Divide 71 by 23. (23 × 3 = 69) r 3 \\ 23 ) 713 \\ -69 \\ 2 Step 2: Bring down the next digit, 3. Divide 23 by 23. (23 × 1 = 23) r 31 \\ 23 ) 713 \\ -69 \\ 23 \\ -23 \\ 0 The quotient is 31 with a remainder of 0. So, (713)/(23) = 31. Final Answer: 31