Vedic Maths

Sutra 1

There is a square field, each size measuring 75 meters. If we have to cover the field with grass at

the cost of Rs. 75/- per sq. meter. What will be the total cost?

752

752 = 5625

752 means 75 x 75.

The answer is in two parts: 56 and 25.

The last part is always 25.

The first part is the first number, 7, multiplied by the number "one more", which is 8:so 7 x 8 = 56

852

852 = 7225

8 x 9 = 72.

Method for multiplying numbers where the first figures are the same and the last figures add up to 10.

32 x 38 =

32 x 38 = 1216

Both numbers here start with 3 and the last figures (2 and 8) add up to 10.

So we just multiply 3 by 4 (the next number up) to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to get the last part of the answer.

81 x 89 =

81 x 89 = 7209

Sutra 2

21 x 23 =

21 x 23 = 483

This is normally called long multiplication but actually the answer can be written straight down using the VERTICALLY AND CROSSWISEformula. We first put, or imagine, 23 below 21:

There are 3 steps:a) Multiply vertically on the left: 2 x 2 = 4.    This gives the first figure of the answer.b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8    This gives the middle figure.c) Multiply vertically on the right: 1 x 3 = 3    This gives the last figure of the answer.

Similarly 61 x 31 = 1891

6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

If you want 21 stamps at 26 Rupees each. What is the total cost?

33 x 44 =

Vertically on the left we get 12.

Crosswise gives us 24, so we carry 2 to the leftand mentally get 144.

Then vertically on the right we get 12 and the 1here is carried over to the 144 to make 1452.

Sutra 3

Multiplying a number by 11.

To multiply any 2-figure number by 11 we just putthe total of the two figures between the 2 figures.

26 x 11 = 286 Notice that the outer figures in 286 are the 26being multiplied.And the middle figure is just 2 and 6 added up.

So 72 x 11 = 792

77 X 11 = ?

77 x 11 = 847

This involves a carry figure because 7 + 7 = 14

we get 77 x 11 = 7147 = 847.

234 x 11 =

234 x 11 = 2574

We put the 2 and the 4 at the ends.

We add the first pair 2 + 3 = 5.

and we add the last pair: 3 + 4 = 7.

SQUARES50²= 2500

51² = 2601 49² = 240152² = 2704 48² = 230453² = 2809 47² = 220954² = 2916 46² = 211655² = 3025 45² = 202556² = 3136 44² = 193657² = 3249 43² = 184958² = 3364 42² = 176459² = 3481 41² = 168160² = 3600 40² = 1600

Sutra 4

Squares and Cubes

• (a+b) ²=a²/2ab/b²• (98) ²= 81/144/64 =9604• (127) ²= 144/168/49 = 16129

• (a+b)³ =a³/3a²b/3ab²/b³• (54) ³ = 125/300/240/64 =157464