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प्रश्न
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
54
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उत्तर
Here, a = 5, b = 4
Step 1. Make 3 columns and write the values of a2, 2 x a x b and b2 in these columns.
| Column I | Column II | Column III |
| a2 | 2 x a x b | b2 |
| 25 | 40 | 16 |
Step 2. Underline the unit digit of b2 (in Column III) and add its tens digit, if any, with 2 x a x b (in Column II).
| Column I | Column II | Column III |
| a2 | 2 x a x b | b2 |
| 25 | 40 + 1 | 16 |
| 41 |
Step 3. Underline the unit digit in Column II and add the number formed by the tens and other digits, if any, with a2 in Column I.
| Column I | Column II | Column III |
| a2 | 2 x a x b | b2 |
| 25 + 4 | 40 + 1 | 16 |
| 29 | 41 |
Step 4. Underline the number in Column I.
| Column I | Column II | Column III |
| a2 | 2 x a x b | b2 |
| 25 + 4 | 40 + 1 | 16 |
| 29 | 41 |
Step 5. Write the underlined digits at the bottom of each column to obtain the square of the given number.
In this case, we have:
542 = 2916
Using multiplication:
54
54
216
270
2916
This matches with the result obtained using the column method.
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