## 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:

8^{2} = (10-2)^{2} = 100 – 40 + 4 = 10(10-4) + 4

= 10(10-2-2) + 2^{2} = 10(8-2) + 2^{2} = **(8-2)/2 ^{2}** = 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:

- 9
^{2}= (9-1)/1^{2}= 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**1**^{2}= 1 .

Final Answer:**81** - 13
^{2}= (13+3)/3^{2}= 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**3**^{2}= 9

Final Answer:**169** - 18
^{2}= (18+8)/8^{2}= 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**8**. As we are using Base 10, 6 gets carry forwarded to other side.^{2}= 64

Final Answer:**324**

Similarly, T*rick to square number using Yavadunam which is closer to 100/1000 (Base 100/1000) is:*

- 93
^{2}= (93-7)/7^{2}= 86/49 = 8649 - 89
^{2}= (89-11)/11^{2}= 78/121 = 7921 - 113
^{2}= (113+13)/13^{2}= 126/169 = 12769 - 1002
^{2}= (1002+2)/2^{2}= 1004/004 = 1004004

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