Square Using Column Method


 
 
Concept Explanation
 

Square Using Column Method

This method is convenient for finding squares of two digit numbers only.As the number of digits increases ,this method becomes difficult and time-consuming.This method uses the identity large (a+b)^{2}=a^{2}+2ab+b^{2} for finding the square of a two digit number ab (where a is the tens digit and b is the units digit).

We follow the following steps to find the square of a two digit number ab (where a is the tens digit and b is the units digit).

Step I: Make three columns and write the value of large a^{2},2times atimes b ;and; b^{2}  respectively in these columns as follows :

As an illustration let us take ab = 57.

large therefore a = 5;and;b=7 .

Column I Column II Column III
large a^{2} large 2 times atimes b large b^{2}
25 70 49

Step II :  Underline the units digit of large b^{2} ( in column III ) and add its ten digit,if any,to large 2 times atimes b( in column II )

Column I

large a^{2}

Column II

large 2 times atimes b

Column III

large b^{2}

25

70

+4

large 4underline{9}
  74  

Step III : Underline the unit digits in column II and add the number formed by tens and other digit , if any , to large a^{2} in column I.

Column I

large a^{2}

Column II

large 2 times atimes b

Column III

large b^{2}

25

+7

70

+4

large 4underline{9}

 

32 large 7underline{4}  

Step IV:  Underline the number in column I

Column I

large a^{2}

Column II

large 2 times atimes b

Column III

large b^{2}

25

+7

large underline{32}

70

+4

large 7underline{4}

large 4underline{9}

 

 

32 4 9

Step V: Write the underlined digits at the bottom of each column to obtain the square of the given number.

In this case ,we have large (57)^{2}=3249

Illustration: Find the square of 96 using column method.

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Sample Questions
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Question : 1

Find the ten's digit of the number obtained in the column II while finding the square of 88.

Right Option : C
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Explanation
Question : 2

Find the ten's digit of the number obtained in the column II while finding the square of 79.

Right Option : B
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Explanation
Question : 3

Find the square of 99 using column method.

 

Right Option : B
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Explanation
 
 


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