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Square of a Number Ending With 5 As a Unit Digit:

 

Suppose the Number Ends with 5 as Unit Digit is (a5) then (a5)^2 is

a(a+1)/25

FOR EXAMPLE :

                                    25^2 is 2(2+1)/25 i.e 2(3)/25 and the final answer is 625

                                   95^2 is 9(9+1)/25 i.e 9(9+1)/25 and final answer is 9025

 

Square of a Number Using Algebraic Identities :

(a+b)^2=a^2+b^2+2ab

EXAMPLE:

36^2=(35+1)^2 i.e 35^2 + 1^2 +2(35)(1)

              1225+1+70=1296

Square of Numbers Close to 50:

(50+a)^2=100(25+a)+a^2

(50-a)^2=100(25-a)+a^2

Example:

54^2=(50+4)^2=100(25+4)+16=2916

          45^2=(50-5)^2=100(25-5)+25=2025   

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