## Saturday, July 29, 2006

### Vedic Maths - Squares n Cubes

1. Squares:

1.1. Squares ending in 5:

Separate >> a | 5

Eg 352 >> 3 | 5 >> (3 X 4) | 25 >>1225

Sly, 452 >> 4 | 5 >> 20|25 >> 2025

1.2. General case:

Use Cross-multiply method of multiplication explained in previous post.

2. Cubes: (2 digit no >> ab3)

{a + b)3 = a3 + 3a2b + 3ab2 + b3

= a3 + a3(b/a)1 + a3(b/a)2 + a3(b/a)3 ……… (1)

+ 2 a2b + 2 ab2 …….. (2)

Modus Operandi:

i. Split no as a | b

ii. Find a3 and ratio b/a

iii. From this we get eq (1) by

We get next no by multiplying current no by the ratio b/a.

Left most no is a3.

iv. We get eq (2) by multiplying middle two terms of eq (1) by 2

Eg. 273

Here a = 2, b = 3

Therefore, a3 = 8 , b/a = 7/2 (=3.5)

Therefore eq (1) = 8 | 28 | 98 | 343

(8 X 3.5 = 28, 28 X 3.5 = 98, 98 X 3.5 = 343)

eq (2) = | 56 | 196 |

(28 X 2 = 56, 98 X 2 = 196)

Sum = 8 | 84 | 294 | 343

Since only 1 digit can be inside on bar, carry forward

8 | 84 | 294 | 343

8 | 84 | 328 | 3

8 | 116 | 8 | 3

19 | 6 | 8 | 3

Therefore, 273 = 19683