Vedic Mathematics - First Suthra (Ekadhikena Purvena) : Algebraic Proof

 

Vedic Mathematics

Suthra 1     :        Ekadhikena Purvena (Algebraic Proof)

Meaning    :        By One More than the Previous One

Let us consider

(ax + b)² = a²x² + 2abx + b²

To find 15²,

Here x= 10 and b = 5

(10a + 5) ²       =          a².10² + 2.10.a.5 + 5²

                        =          a².10² + a.10² + 5²

                        =          (a² + a) .10² + 5²

                        =          a(a+1). 10² + 25

Here, (10a + 5) represents numbers

(10x1+5)          =          15

(10x2+5)          =          25

(10x3+5)          =          35

(10x4+5)          =          45

(10x5+5)          =          55

(10x6+5)          =          65 etc…..

Thus

75²       =         (70+5)²

            Here b = 5 and a =7

            75²       =          7.(7+1)x10² + 5²

                        =          7x8 ×100+ 25

                        =          5625

Similarly try for 85², 95²