Advertisements
Advertisements
Question
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
54
Advertisements
Solution
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.
RELATED QUESTIONS
Find the square of the given number.
71
What will be the units digit of the square of the following number?
977
What will be the units digit of the square of the following number?
12796
Observe the following pattern
\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) = \frac{2 \times 3 \times 4}{3}\]
\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) = \frac{3 \times 4 \times 5}{3}\]
\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) + \left( 4 \times 5 \right) = \frac{4 \times 5 \times 6}{3}\]
and find the value of(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + (5 × 6)
Observe the following pattern \[1 = \frac{1}{2}\left\{ 1 \times \left( 1 + 1 \right) \right\}\]
\[ 1 + 2 = \frac{1}{2}\left\{ 2 \times \left( 2 + 1 \right) \right\}\]
\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\]and find the values of following:
31 + 32 + ... + 50
Which of the following number square of even number?
324
Which of the following number are square of even number?
6561
Find the squares of the following numbers using diagonal method:
98
For every natural number m, (2m – 1, 2m2 – 2m, 2m2 – 2m + 1) is a pythagorean triplet.
Find the area of a square field if its perimeter is 96 m.
