Question

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

 25

Answer 1

(i) Here, a = 2, b = 5
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
4	20	25

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
4	20 + 2	25
	22

 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
4 + 2	20 + 2	25
6	22

Step 4. Underline the number in Column I.

Column I	Column II	Column III
a2	2 x a x b	b2
4 + 2	20 + 2	25
6	22

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:
25² = 625
Using multiplication:
    25
    25
  125
  50   
 625
This matches with the result obtained by the column method.