Vedic Maths : yavadunam tavadunikrtya varganca yojayet
yavadunam tavadunikrtya varganca yojayet
what ever the deficiency subtract that deficit from the number and write along side the square of that deficit
यावदूनम् तावदूनीकृत्य वर्ग च योजयेत्
We already know
Here, let's take a special case of finding square. A = B , so a = b
A * B = A * A
= x ( x + a + a) + a*a = x ( x + 2a) + a ^ 2
= x [ (x + a) + a] + a ^2
But as we know x + a = A
So, x [ (x + a) + a] + a ^ 2 = x ( A + a ) + a ^ 2
Here, 'a' can be negative also
For example
|
x |
a |
n |
x * [ A + a ) |
a ^ 2 |
A ^ 2 |
|
|
9 |
10 |
-1 |
1 |
1 |
81 |
|
|
8 |
10 |
-2 |
1 |
10 * ( 8 - 2 )
= 60 |
4 |
64 |
|
11 |
10
|
+1 |
1 |
1 |
121 |
|
|
12 |
10 |
+2 |
1 |
10 * ( 12 + 2 )
= 140 |
4 |
144 |
|
13 |
10 |
+3 |
1 |
10
* ( 13 + 3 ) = 160 |
9 |
169 |
|
14 |
10 |
+4 |
1 |
10 * ( 14 + 4 )
= 180 |
16 |
196 |
|
15 |
10 |
+5 |
1 |
10
* ( 15 + 5 ) = 200 |
25 |
225 |
|
19 |
10 |
+9 |
1 |
81 |
361 |
|
|
91 |
100 |
-9 |
2 |
100 * ( 91 - 9 ) =
8200 |
81 |
8281 |
|
94 |
100 |
-6 |
2 |
100
* ( 94 – 6 ) = 8800 |
36 |
8836 |
|
97 |
100 |
-3 |
2 |
100 * ( 97 – 3 ) = 9400 |
9 |
9409 |
|
108 |
100 |
+8 |
2 |
100
* (108 + 8 ) = 11600 |
64 |
11664 |
|
989 |
1000 |
-11 |
3 |
1000 * ( 989 – 11) = 978000 |
121 |
978121 |
|
9989 |
10000 |
-11 |
4 |
10000
* ( 9989 – 11 ) = 99780000 |
121 |
99780121 |
Vedic Maths: Anurupyena
Anurupyena
Proportionality
आनुरूप्येण
Any number can be expressed as : N = x + k, Where x is p * (10 ^ n) and k is remainder if you divide N with 10 ^ n. Here N, n, k are integer. k can be negative also. p is decimal number or integer number. p > 1 or p < 1 both are possible.
Here are the examples:
|
x |
k |
x = p * (10 ^ n) |
p |
n |
N = (x = p * (10 ^ n) ) + k |
|
|
41 |
50 |
-9 |
50
= 0.5 * 100 |
0.5 |
2 |
0.5 * ( 10 ^ 2 ) - 9 |
|
41 |
40 |
+1 |
40 = 4 * 10 |
4 |
1 |
4
* ( 10 ^ 1 ) + 1 |
|
49 |
50
|
-1 |
50
= 0.5 * 100 |
0.5 |
2 |
0.5 * ( 10 ^ 2 ) – 1 |
|
249 |
250 |
-1 |
250 = 0.25 *
1000 |
0.25 |
3 |
0.25
* ( 10 ^ 3 ) – 1 |
|
245 |
250 |
-5 |
250
= 0.25 * 1000 |
0.25 |
3 |
0.25 * ( 10 ^ 3 ) – 5 |
|
229 |
250 |
-21 |
250
= 0.25 * 1000 |
0.25 |
3 |
0.25
* ( 10 ^ 3) - 21 |
|
230 |
250 |
-30 |
250 = 0.25 * 1000 |
0.25 |
3 |
0.25 * ( 10 ^ 3) - 30 |
|
3998 |
5000 |
-1002 |
5000 = 0.5 *
10000 |
0.5 |
4 |
0.5
* ( 10 ^ 4 ) – 1002 |
|
4998 |
5000 |
-2 |
5000 = 0.5 * 10000 |
0.5 |
4 |
0.5 * ( 10 ^ 4 ) – 2 |
|
532 |
500 |
+32 |
500
= 5 * 100 |
5 |
2 |
5
* ( 10 ^ 2 ) + 32 |
|
472 |
500 |
-28 |
500 = 5 * 100 |
5 |
2 |
5 * ( 10 ^ 2 ) – 28 |
