Yaavadunam:

*Whatever the extent of its deficiency*
Yaavadunam is the tenth

sutra of

Vedic mathematics. Its corollary is

Samuccayagunitah. It shares similarities with the sutra

Ekadhikina Purvena and with the upsutras

Yavadunam Tavadunikritya Varga Yojayet and

Anurupyena.

The sutra is used to cube numbers:

**Cubing numbers that are near a power of ten** Such as 13, 104, 1012, etc.

*Example:* 12

^{3}
Step One: Subtract the nearest power of ten from the number: 12 - 10 = 2

Step Two: Double this number and add the number being cubed: (2 x 2) + 12 =

**16**
Step Three: Subtract from this number the power of ten from step one: 16 - 10 = 6

Step Four: Multiply this number by the answer in step one: 2 x 6 =

**12**
Step Five: Cube the answer in step one: 2

^{3} =

**8**
Step Six: Since we're cubing a 2 digit number, add two zeros to the answer in step two: 1600

Step Seven: Add 1 zero to the answer in step four: 120

Step Eight: Add the answers in steps seven and eight to the answer in step five: 1600 + 120 + 8 = 1728

Thus, 12

^{3} = 1728

**Cubing numbers that are near a multiple of a power of ten** Such as 42, 507, 2008, etc.

*Example:* 48

^{3}
Step One: Keep in mind that the

*main base* is 10 and our

*working base* will be 50

Step Two: Divide the main base by the working base: 10 / 50 = 1/5

Step Three: Subtract the working base from the number being squared: 48 - 50 = -2

Step Four: Double this number and add the number being squared: (-2 x 2) + 48 = 44

Step Five: Divide this number by the square of the ratio found in step two: 44 / (1/5)

^{2} = 44 / (1/25) = 44 x 25 =

**1100**
Step Six: Subtract the working base from the answer in step four: 44 - 50 = -6

Step Seven: Multiply the answer in step three by the answer in step six: -2 x -6 = 12

Step Eight: Divide this number by the ratio in step two: 12 / (1/5) = 12 x 5 =

**60**
Step Nine: Cube the answer found in step three: -2

^{3} =

**-8**
Step Ten: Since we're cubing a 2 digit number, add two zeros to the answer in step five: 110000

Step Eleven: Add 1 zero to the answer in step eight: 600

Step Twelve: Add the answers in steps ten and eleven to the answer in step nine: 110000 + 600 + -8 = 110592

Thus, 48

^{3} = 110592

To see more examples of Yaavadunum, 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