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COLUMN AND DIAGONAL METHOD FOR SQUARING A NUMBER
From DEPSSA WiKi

COLUMN METHOD FOR SQUARING
 Step1. Make three columns,I,II and III,headed by _{a}2, (2 x a x b) and _{b}2 respectively.Write the values of_{a}2, (2 x a x b),_{b}2 in columns I,II and III respectively.
 Step2. In column III underline the unit digit of _{b}2 and carry over the tens digit of it to column II and add it to the value of (2 x a x b).
 Step3. In column II underline the units digit of the number obtained in step 2 and carry over the tens digit of it to Column I and add it to the value of _{a}2.
 Step4. Underline the number obtained in Step3 in column I.
The underline digits give the required square number.
 EXAMPLE 1: Find the square of 47.
Solution  Given the number=47
therefore a=4 and b=7
  
  
therefore _{(47)}2 =2209
 EXAMPLE 2: Find the square of 86.
Solution  Given the number=86
therefore a=8 and b=6
  
  
therefore _{(86)}2 =7396
DIAGONAL METHOD FOR SQUARING
Example: Find _{(72)}2 using the diagonal method.
SOLUTION:
 Step 1.The given number contains two digits. So, draw a square and divide it into 4 subsquares as shown below.Write down the digits 7 and 2 horizontally and vertically, as shown below.
 Step 2.Multiply each digit on the left of the square with each digit on the top, one by one.Write the product in the following subsquares.If the product is a onedigit number,write it below the diagonal.In case of two digit number, write the tens digit above the diagonal and units digit below the diagonal.
 Step 3.Starting below the lowest diagonal, sum the digits diagonally.
If the sum is a twodigit number,underline the units digit and carry over the tens digit to the next diagonal.
 Step 4.Underline all the digits in the sum above the topmost diagonal.
 Step 5.The underlined digits give the required square number.
Therefore, _{(72)}2 =5184
SIMPLE METHOD FOR SQUARING
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 _{(47)}2
4 X 4 = 16
7 X 7 = 49
Both digit Multiplying and Multiplying with 2
4 X 7 X 2 = 56
In 56 add Zero
560 + 1649 = 2209
 _{(64)}2
6 X 6 = 36
4 X 4 = 16
6 X 4 X 2 = 48
480 + 3616 = 4096
 _{(87)}2
8 X 8 = 64
7 X 7 = 49
8 X 7 X 2 = 112
1120 + 6449 = 7569
MODULE CREATED BY
UMESH KUMAR
TEACHER, UPG. MIDDLE SCHOOL SAGARBHANGA
DUMKA, JHARKHAND
SOURAV KUMAR
DUMKA, JHARKHAND