Yavadunam Tavadunikritya Varga Yojayet:

*Whatever the Deficiency Subtract that Deficit from the Number and Write Along Side the Square of that Deficit*
Yavadunam Tavadunikritya Varga Yojayet is the corollary to

Sankalana - Vyavakalanabhyam, the seventh

sutra of

Vedic mathematics.

This sutra, similar to

Anurupyena and

Ekadhikina Purvena, can be used to find the square or the cube of a number near base powers of 10, such as 99, 992, 9997, etc.

**Squaring a number slightly lower than a power of 10:**
*Example: *996

^{2}
Subtract the number from the nearest power of ten:

1000 - 996 = 4

Subtract this

deficit from the number: 996 - 4 = 992

Since the nearest power of ten is 1000, add three zeroes to this result: 992,000

Square the deficit: 4 x 4 = 16

Add this to 992,000 to get the answer

996

^{2} = 992,016

**Squaring a number slightly higher than a power of 10:**
*Example:* 10025

^{2}
Subtract the nearest power of 10 from the number:

10025 - 10000 = 25

Add this

surplus to the number: 10025 + 25 = 10050

Since the nearest power of ten is 10000, add four zeroes to this result: 100,500,000

Square the surplus: 25 x 25 = 625 (use

Ekadhikina Purvena to quickly square any number ending in 5)

Add this to 100,500,000 to get the answer

10025

^{2} = 100,500,625

**Cubing a number slightly lower than a power of 10:**
*Example:* 998

^{3}
Subtract the nearest power of 10 from the number to find the deficit: 998 - 1000 = -2

Double the deficit and add it to the number: 998 + (2 x -2) = 994

Since the power of 10 we are working from is 1000, add three zeroes to 994 to get our temporary answer:

**994000**
Subtract our power of 10 from 994: 994 - 1000 = -6

multiply this number by the deficit in the first step: -2 x -6 = 12

Add this number (12) to our temporary answer:

**994012**
Then add three more zeroes:

**994012000**
Cube the deficit from the first step: -2

^{3} = -8

Add this to our temporary answer to arrive at our final answer: 99401200 + -8 =

**994011992**
**Cubing a number slightly higher than a power of 10:**
*Example:* 107

^{3}
Subtract the nearest power of 10 to find the surplus: 107 - 100 = 7

Double the surplus and add it to the number: 107 + (2 x 7) = 121 Because the power of 10 we are working from is 100, add two zeroes to this number for our temporary answer:

**12100**
Subtract from 121 the power of ten from the first step: 121 - 100 = 21

Multiply this number by the surplus in the first step: 21 x 7 = 147

Add this number to our temporary answer: 12100 + 147 =

**12247**
Add two more zeroes to the temporary answer:

**1224700**
Cube the surplus from the first step: 7

^{3} = 343

Add this to the temporary answer to arrive at the final answer: 1224700 + 343 =

**1225043**
This sutra can also be applied to numbers that are near a multiple of a power of ten, such as 402, which is near (4 x 100). To learn more about Yavadunam Tavadunikritya Varga Yojayet, check out the resources below.

**RESOURCES:**

*Vedic Mathematics* by Sri Bharati Krisna Tirthaji

http://www.vedamu.org/Mathematics/course.asp

http://www.sanalnair.org/articles/vedmath/intro.htm

http://www.vedicganita.org/ganitsutras.htm

http://hinduism.about.com/library/weekly/aa062901a.htm

http://www.vedicmaths.org/

http://www.hinduism.co.za/vedic.htm

*Mathemagics* by Arthur Benjamin and Michael B. Shermer

http://en.wikipedia.org/wiki/Vedic_math

http://www.tifr.res.in/~vahia/dani-vmsm.pdf

http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html