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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.
संबंधित प्रश्न
Find the square of the given number.
46
What will be the units digit of the square of the following number?
12796
From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ... n = n2, where the left hand side consists of n terms.
Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
52 + 62 + 72 + 82 + 92 + 102 + 112 + 122
The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is ______.
The sum of first n odd natural numbers is ______.
If x and y are integers such that x2 > y2, then x3 > y3.
Write two Pythagorean triplets each having one of the numbers as 5.
Find the length of the side of a square if the length of its diagonal is 10 cm.
Find the area of a square field if its perimeter is 96 m.
