To find the square root of 1 75/1369 using the long division method, we proceed as follows:
Step 1: Group the digits in pairs starting from the decimal point:
0175 | 1369
Step 2: Find the largest digit, let's call it 'x', such that x * x is less than or equal to the first group of digits (01 in this case). In this case, x = 1 since 1 * 1 = 1. Place x as the first digit in the quotient.
Step 3: Subtract the square of the digit from the first group of digits, and bring down the next pair of digits (75 in this case) to the right of the result.
1
______
√0175 | 1369
- 01
______
09 75
Step 4: Double the first digit of the quotient (2 * 1 = 2), and assume it as the divisor. Find the largest digit, let's call it 'y', to fill the blank such that when the new divisor is multiplied by y and added to itself, the result is less than or equal to the current dividend (975 in this case). In this case, y = 4 since 24 * 4 = 96. Place y as the next digit in the quotient.
14
______
√0175 | 1369
- 01
______
09 75
- 09 60
_______
15
Step 5: Repeat steps 3 and 4 until all the digits in the dividend have been used.
141
______
√0175 | 1369
- 01
______
09 75
- 09 60
_______
15 09
Step 6: The resulting number is the square root of 1 75/1369. Therefore, √1 75/1369 = 1.409.
Hence, the square root of 1 75/1369, using the long division method, is approximately 1.409.
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Answer:
To find the square root of 1 75/1369 using the long division method, we proceed as follows:
Step 1: Group the digits in pairs starting from the decimal point:
0175 | 1369
Step 2: Find the largest digit, let's call it 'x', such that x * x is less than or equal to the first group of digits (01 in this case). In this case, x = 1 since 1 * 1 = 1. Place x as the first digit in the quotient.
Step 3: Subtract the square of the digit from the first group of digits, and bring down the next pair of digits (75 in this case) to the right of the result.
1
______
√0175 | 1369
- 01
______
09 75
Step 4: Double the first digit of the quotient (2 * 1 = 2), and assume it as the divisor. Find the largest digit, let's call it 'y', to fill the blank such that when the new divisor is multiplied by y and added to itself, the result is less than or equal to the current dividend (975 in this case). In this case, y = 4 since 24 * 4 = 96. Place y as the next digit in the quotient.
14
______
√0175 | 1369
- 01
______
09 75
- 09 60
_______
15
Step 5: Repeat steps 3 and 4 until all the digits in the dividend have been used.
141
______
√0175 | 1369
- 01
______
09 75
- 09 60
_______
15 09
Step 6: The resulting number is the square root of 1 75/1369. Therefore, √1 75/1369 = 1.409.
Hence, the square root of 1 75/1369, using the long division method, is approximately 1.409.
√1(75/1369)
√1444/1369
44/37