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COLUMN AND DIAGONAL METHOD FOR SQUARING A NUMBER

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COLUMN METHOD FOR SQUARING

  • Step-1. Make three columns,I,II and III,headed by a2, (2 x a x b) and b2 respectively.Write the values ofa2, (2 x a x b),b2 in columns I,II and III respectively.
  • Step-2. In column III underline the unit digit of b2 and carry over the tens digit of it to column II and add it to the value of (2 x a x b).
  • Step-3. 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 a2.
  • Step-4. Underline the number obtained in Step-3 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

I
II
III
a2
(2 x a x b)
b2
16
+6
22
56
+4
60
49


therefore (47)2 =2209

  • EXAMPLE 2:- Find the square of 86.

Solution - Given the number=86

therefore a=8 and b=6

I
II
III
a2
(2 x a x b)
b2
64
+9
73
96
+3
99
36


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 one-digit 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 two-digit 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.


image:Figure math.jpg


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

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