How to solve numbers with minimal calculations or mentally .Here we will discuss some more cases , where numbers are just half the base(10)
Or we can say near 5,50,500,5000,50000 etc.
Case 1.
41 x 41
Here we will take base as 50 (100÷2)
41-9
41-9
---------
41-9/9×9
32/81
But as we have assumed base as 50 because numbers are closer to 50. Base 50 is half of 100, so we will divide the answer by 2.
32÷2/81
16/81
= 1681 is answer.
Or
Another way to solve the same problem .
41x41
Assume base as 10
10 x 5=50
41-9
41-9
---------
32/81
X 5/
---------
160/81
As we have taken base 10 . So 8 will be carried over.
168/1
1681 answer.
Why we have multiplied the above with 5. So if u are wondering then the answer is because we have taken the base as 10 and the number are closer to 50 base and to make it 50 we have multiplied it by 5. Thus we have to multiply the answer by 5.
Or
Another way if you want to assume base as 40 because numbers are 41 x 41
Then 10 x 4= 40
So,
41 + 1
41 + 1
----------
41+1/1×1
42/1
×4
--------
168/1
1681 answer.
EXAMPLE::
1. 49 x 49
Working base 100/2
49-1
49-1
--------
48/01
÷ 2
----------
24/01=2401
Or
Working base 10x5
49-1
49-1
-----------
48/1
×5
-----------
240/1
2401 answer.
Example 2
23 x 21
Working base 10 x 3= 30
23 - 7
21 - 9
-------------
23-9/ 7x9
14/63
×3
-------------
42/63
6 will be carried over because of base 10
48/3
483
Or
Working base 10x2
Then
23+3
21+1
---------
24/3
×2
--------
48/3
483 answer.
● Direct short cut for square. Using the first corollary which is arising out of the 'Nikhilam ' Sutra means : whatever the extent of its deficiency, lessen it still further to that very extent and also set up the square of that deficiency.
A. 9x9
9-1
9-1
-------
9-1/1×1
8/1
81
B. 7 x 7
(7-3)/3^2
4/9=49
C. 11^2 = (11+1)/1^2=121
D. 12^2=(12+2)/2^2= 144
E. 13^2 =(13+3)/3^2=169
F. 14^2 =(14+4)/4^2= 18/16=196
G . 15^2 =(15+5)/5^2= 20/25=225
And so on.....
In the next post we will learn how to write table quickly ... by using simple techniques of the same sutra....rather than memorizing it....
Keep learning. Keep smiling 😊😊😊
