Vedic Maths - Squares n Cubes

1. Squares:

1.1. Squares ending in 5:

Separate >> a | 5

Answer : a(a+1) | 25

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

v. Add only corresponding terms.

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