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Find the square of the following numbers using the duplex method.
148
148
- a)8314
- b)21904
- c)8514
- d)8614
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find the square of the following numbers using the duplex method.148a)...
Step-by-Step Explanation:
Given Number: 148
1. Decomposition:
- Write the number as 100a + 10b + c
- For 148, a = 1, b = 4, c = 8
2. Duplex Calculation:
- Add the last digit (c) to the square of the first digit (a^2) and write the result in the unit's place.
- For 148, 8 + 1^2 = 9 (Write 9 in the unit's place)
- Double the product of the first and last digit (2 * a * c) and add it to the product of the first and second digit (2 * a * b) and write the result in the ten's place.
- For 148, 2 * 1 * 8 + 2 * 1 * 4 = 16 + 8 = 24 (Write 4 in the ten's place and carry over 2)
- Add the carried-over number (if any) to the square of the middle digit (b^2) and write the result in the hundred's place.
- For 148, 2 + 4^2 = 18 (Write 8 in the hundred's place)
- If there is a carry in the hundred's place, carry it over to the thousand's place.
3. Square of the Given Number:
- Combine the results from the duplex calculation to get the square of the given number.
- For 148, the square is 21904.
Therefore, the square of 148 using the duplex method is 21904.
Given Number: 148
1. Decomposition:
- Write the number as 100a + 10b + c
- For 148, a = 1, b = 4, c = 8
2. Duplex Calculation:
- Add the last digit (c) to the square of the first digit (a^2) and write the result in the unit's place.
- For 148, 8 + 1^2 = 9 (Write 9 in the unit's place)
- Double the product of the first and last digit (2 * a * c) and add it to the product of the first and second digit (2 * a * b) and write the result in the ten's place.
- For 148, 2 * 1 * 8 + 2 * 1 * 4 = 16 + 8 = 24 (Write 4 in the ten's place and carry over 2)
- Add the carried-over number (if any) to the square of the middle digit (b^2) and write the result in the hundred's place.
- For 148, 2 + 4^2 = 18 (Write 8 in the hundred's place)
- If there is a carry in the hundred's place, carry it over to the thousand's place.
3. Square of the Given Number:
- Combine the results from the duplex calculation to get the square of the given number.
- For 148, the square is 21904.
Therefore, the square of 148 using the duplex method is 21904.
Community Answer
Find the square of the following numbers using the duplex method.148a)...
Splitting the number 92 into its tens and units place digits, we have 9 and 2. Calculating the cross product and the square of each digit:
Cross product: 9 * 2 = 18
Square of 9: 92 = 81
Square of 2: 22 = 4
Square of 9: 92 = 81
Square of 2: 22 = 4
Combining the results, we get 8414, which is the square of 92. Among the options, (b) 8414 is the correct answer.
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