## Vedic Math – Squares of Numbers

### How to Find Squares of Single Digit or 2 Digit Numbers.

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

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 ^{2}= 64**. As we are using Base 10, 6 gets carry forwarded to other side.

Final Answer:

**324**{Where First term at tens place and last term at Units place}

It is a specific and shortcut to square numbers is closer to power of 10. (10, 100, 1000, ….)

**Square of 14:**

14^{2} = (14+4)/4^{2} = 18/16 = 196

Here 14 is 4 more than 10(Base 10), So **Excess = 4**

Increase it still further to that extent, So **(14+4) = 18**

Square its excessive, So **4 ^{2}= 16**

Final Answer:

**196**

**Square of 97:**

97^{2} = (97-3)/3^{2} = 94/09 = 9409

Here 97 is 3 less than 100(Base 100), So **deficiency =3**

Reduce it still further to that extent, So **(97-3) = 94.**

Square its deficiency, So **3 ^{2} = 09.** (As base is 100, we need exactly 2 digits. Hence 09).

Final Answer:

**9409**

**Practice :**

- 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