Squaring Made Easy
H.D. Motiramani
Two step method of squaring any two digit number is very easy. In first step we square both the digits individually. For example if we were to find out square of 27, we, as a first step, square 2 and 7 individually and keep them as a result of first sstep. 2²= 4 on left hand side and 7²=49 on right hand side. In step two this new number (result of step 1) is to be maneuvered slightly by adding the multiplication of twice of 2,7 and10.
Therefore in this example of 27² , the square of 27 will be 2² (equal to 4 on Left hand side) followed by 7²=49 on right hand side. So 449 is the answer of step 1 .
In second step this number 449 needs to be added by a number equal to 2×2×7×10=280.
The answer of 27² will therefore be 449+280=729.
One thing to note in this method is that the square of unit digit that is the right side digit of the number to be squared has to be in two digits. For example, if there is 1² = 1, it will be treated as 01. Likewise, the square of 3, if it is a unit digit, will be treated as 09. The method will be pretty clear by way of following examples.
Examples:
(a) 31²:
Step1: 3 and 1 need to be squared separately.
Answer of 3² is to be kept on left hand side followed by answer of 1²= 01 on right hand side. So
901 is the result of step1.
Step2: Answer of step 1 needs to be added by a number equal to 2×3×1×10=60
The answer of 31² will be 901+60=961
(b) 97²:
Step1: 9² =81 to be a part of left hand side and 7²=49 to be on right hand side. So 8149 is the result of step1.
Step2: 2×9×7×10=2×630=1260 needs to be added in the result of step 1.
So the answer of 97²= 8149+1260=9409
(c) 126²:
Step1: In such cases number 12 (combined 1 and 2) can be treated as 1st digit and 6 as second digit. So the answer of step 1 will be 12²=144 on LHS, 6²=36 on RHS. Result of step 1 will be 14436.
Step2: 2×12×6×10= 12×12×10=1440
So the answer will be 14436+1440=15876
(d) 743²:
Step1: LHS will be 74² and RHS will be 3²=09
Now to get the answer to 74² let us follow the method of square of 2 digits where we need to place 7² on LHS and 4² on RHS. Thus 4916 to be added with 2×7×4×10=560. 74² will therefore be 4916+560=5476.
The answer of 743² will therefore be 547609 (Step1 answer)to be added with 2×74×3×10=4440.
Step 2: 547609+4440=552049 will therefore be the answer of 743²
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