Squaring
of a number is largely used in mathematical calculations. There are so many
rules for special cases. But we will discuss a general rule for squaring which
is capable of universal application.
From
our childhood we all know one common formula.
i.e
(a+b)2 = a2+2ab+b2
We
can calculate squares using above formula. So let us do some examples
242=???
To
calculate squares by using above formula we have to follow some steps.
i.e
let us take unit digit as ‘b’ and remaining part as ‘a’.
in
24, a=2 and b=4.
We
should start our calculation from the right side of the formula.
Step-1:
b2=16
242= 6 and 1 as reminder.
Step-2:
2ab=2x2x4=16
242= 76 and 1 as reminder. (16+1=17)
Step-3:
a2=4
242= 576 (answer).
This
model is time taking to explain but it is very easy to calculate. Now we do
some exercise.
Calculate
squares for the following numbers.
27,
36, 85, 99
Now
how are you feeling? Is it hard or easy??
But
it has some limits. It is useful up to 99 only. We can calculate squares more
than 99 by using this formula but it seems some difficult. So we need to have
some easy and it should satisfy all the conditions.
Now
we are moving to next method which is very useful to calculate square of any
number whether it is 3 digits or 5 digits.
i.e
Duplex Combination Process
Here
I’ll explain this method with an example
8972=???
Explanation:
1. Square of unit digit. i.e 72=49; writte down 9
and carry over 4.
2. 2x9x7=126+4=130; writte down 0 and carry over 13. (ten
digit and unit digit)
3. 2x8x7+92=112+81=193+13=206; writte down 6 and
carry over20. (ten digit square and multiplication of unit digit and hundred
digit.
4. 2x8x9=144+20=164; writte down 4 and carry over 16.
5. 82=64+16=80
So the final answer is 804609.
Lets
we do another example
14322=????
Ans: 210253026124
Explanation:
1. 22=4; Write it down.
2. 2x3x2=12; write down 2 and carry over 1
3. 2x4x2+32=25+1=26; write down 6 and carry over
2.
4. 2x1x2+2x4x3=28+2=30; write down 0 and carry over 3.
5. 2x1x3+42=22+3=25; write down 5 and carry over
2.
6. 2x1x4=8+2=10; write down 0 and carry over 1.
7. 12+1=2
Final Answer is 2050624
So now Practice some squares…
123452=??
875322=??
And do your own numbers…
Some special cases….
A)
Square of a number with unit digit as 5
It is very easy to calculate square of a number with unit
digit as 5. Lets take an example.
252=???
Ans is 625.
Explanation: 52=25; write down 25
Next number for remaining digit 2 is 3. Multiply 2and 3
we get 6. Now write down.
The final answer is 625…
Lets try following numbers…
35,45,75,95,115
Square of a number
which is nearer to 10x
For this type of numbers we use following formula
(a+b)2=a2+2ab+b2
(a-b)2=a2-2ab+b2
Ex:
1) 982=??
98=100-2
(100-2)2=10000-400+4=9604
2) 1072=(100+7)2=10000+1400+49=11449
3) 9982=??
4) 100082=??
Today we end over topic. Tomorrow we discuss about
finding cubes…..
