H.D. Motiramani
Squaring a number ending with 5 is very easy. A simple trick will give us the desired result. Let us learn the same through some examples.
75² =?
Invariably the right hand part of the answer will be 25.
Now, for the trick for left hand side of the answer we multiply the first digit that is 7 in this case with the next integer. Because in the present case first digit on the left hand side is 7 it needs to be multiplied by 8. 7 multiplied by 8 will give 56 which is the left hand part of the answer. So 75²=5625
Likewise for another example of say 35²
Right hand side will be 25 and left hand side will be 3×4=12
So our answer of 35² will be 1225.
If the procedure becomes clear all such squares of two digit numbers ending with 5 can be done in mind quickly. Let us take one more example of say 95².
We place 25 as usual as right hand side of the answer and for left hand side of the answer 9×10=90
So, 95²= 9025
This simple trick of multiplication of two digit numbers can be used for multiplication of two numbers whose first digit is same and the sum total of right hand side number is 10. For example in the case of 19×11 or 57×53 or 76×74 or say 23×27 where LHS digit of both numbers to be multiplied is same and sum total of RHS digits of two numbers totals to 10.
Example: 19*11
Right hand side (RHS) will be simple multiplication of 9*1 =09 in two digits. Left Hand Side (LHS) will be first digit of any of 19 or 11 that is 1 multiplied by next integer 2, so 1*2=2 will be LHS of the answer. Thus the answer will be LHS RHS or 209
Example: 57*53
RHS will be in two digits and simple multiplication of 7 & 3 =21
LHS will be first digit of any of the two numbers 5 multiplied by next integer that is 6 in this case.
So LHS = 5*6=30 Thus the answer 57*53 =3021
Example: 76*74
RHS will be in two digits and simple multiplication of 6 & 4 =24
LHS will be first digit of any of the two numbers multiplied by next integer that is 8 in this case = 7*8=56
So the answer76*74 = 5624
Example: 23*27
RHS will be in two digits and simple multiplication of 3 & 7 =21
LHS will be first digit of any of the two numbers multiplied by next integer that is 3 in this case = 2*3=6
So the answer 23*27 =621
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