Square: If a number is multiplied with itself, then the result of this multiplication is called the square of that number. 

Example: Square of 7 = 7 x 7 = 49

Check: Properties of square of a number

Different methods to find Square of a number

There were different methods to find the square of a number and the methods were:

Multiplication method for finding square: By multiplication method process for finding square of any two digit number is discussed below by the following steps.

Step I  Square the unit digit. { If the square has two digits, then write ten’s digit as carry.}
Step II 2 * Tens digit * units digit + carry
Step III (Tens digit)2 + carry from step II
Step IV Now arrange numbers first write step III , then step II and at units place step I .

For example: Find the Square of 74
Step I (4)2 = 16 { carry 1}
Step ii 2 * 7 x 4 +1 = 57 {carry 5}
Step iii (7)2 + 5 = 49 + 5 = 54
Step iv (74)2 = 5476

Algebraic Method for finding square of a number

To calculate square by this method, two formula are used.
1)    (a+b)2 = a2 + b2 + 2ab

2)    (a-b)2 = a2 + b2 - 2ab

For example: The square of 34

34 can be written as (30+4) in algebraric form
i.e. (30+4)2 = 302 + 42 + 2 * 30 * 4

Check: How to find nth power of  of any number ; Proofs and origin of all the formulas

Square of Decimal Numbers


To find the Square of any decimal number, write the square of the number ignoring the decimal and  then place the decimal twice the place original number starting from unit’s place.

For Example: The Square of 3.5 is as follows

 

method-to-find-square

Since,                (35)2 = 1225
Here, the decimal is after one-digit in 3.5. Hence, the decimal will be placed twice the place of original number in the result.,
Therefore, (3.5)2 = 12.25


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