Question

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication: 

 54 

Answer 1

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.