Yavadunam Tavadunikritya Varga Yojayet
Shortcut method in Vedic Mathematics to square a number when it is closer to power of 10 (10/100/1000…)
Commonly called as Yavadunam Sutra
Sanskrit Name:
यावदूनम् तावदूनी्क्रूत्य वर्ग च् योजयेत्
English Translation:
Square its Deficiency i.e. Whatever the extent of its deficiency/excess is, reduce/increase it still further to that extent and also square its deficiency/excess.
Specific Condition Required:
Numbers need to be close* to power of 10 (10, 100, 1000, etc).
Example with proof:
82 = (10-2)2 = 100 – 40 + 4 = 10(10-4) + 4
= 10(10-2-2) + 22 = 10(8-2) + 22 = (8-2)/22 = 64
{Where First term at tens place and last term at Units place}
Also Check, more Shortcuts to Square a number in Vedic Mathematics.
More Examples:
- 92 = (9-1)/12 = 8/1 = 81
Here 9 is 1 less than 10(Base 10), So deficiency =1
Reduce it still further to that extent, So (9-1) = 8.
Square its deficiency, So 12 = 1 .
Final Answer: 81 - 132 = (13+3)/32 = 16/9 = 169
Here 13 is 3 more than 10(Base 10), So Excess = 3
Increase it still further to that extent, So (13+3) = 16
Square its excessive, So 32= 9
Final Answer: 169 - 182 = (18+8)/82 = 26/64 = 32/4 = 324
Here 18 is 8 more than 10(Base 10), so Excess = 8
Increase it still further to that extent, So (18+8) = 26
Square its excessive, So 82= 64. As we are using Base 10, 6 gets carry forwarded to other side.
Final Answer: 324
Similarly, Trick to square number using Yavadunam which is closer to 100/1000 (Base 100/1000) is:
- 932= (93-7)/72 = 86/49 = 8649
- 892= (89-11)/112 = 78/121 = 7921
- 1132 = (113+13)/132 = 126/169 = 12769
- 10022 = (1002+2)/22 = 1004/004 = 1004004
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