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

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