Question

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

37 

Answer 1

Here, a = 3, b = 7
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
9	42	49

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
9	42 + 4	49
	46

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
9 + 4	42 + 4	49
13	46

Step 4. Underline the number in Column I. 

Column I	Column II	Column III
a2	2 x a x b	b2
9 + 4	42 + 4	49
13	46

 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:
37² = 1369
Using multiplication:
    37
    37
  259
111  
1369
This matches with the result obtained using the column method.