square of numbers using vedic mathematics

Square of numbers using vedic mathematics

We can find the Square of any number in just less than 5 sec 

Square of numbers ending with ones place digit as 5 (up-to 95)

• add one to tens place number and multiply by tens digit / ones place square

15² = 1 x 2 / 5 x 5          =  2 / 25    = 225

45² = 4 x 5 / 5 x 5          =  20 / 25    = 2025 

55² = 5 x 6 / 5 x 5          =  30 / 25    = 3025

75² = 7 x 8 / 5 x 5          =  56 / 25    = 5625

95² = 9 x 10 / 5 x 5          =  90 / 25    = 9025

Square of any number  (up-to 99)

• tens place square / tens x ones x 2 / ones square

23² = 2² / 2x3x2 /3²   =  5 / 2¹  (12)/ 9   = 5,2,9 =529

58² = 5² / 5x8x2 / 8²  =  33 / 6⁸  (86)/ 4⁶ (64)  = 33,6,4 =3364

  

48² = 4² / 4x8x2 / 8²  =  23 / 0⁷  (70)/ 4⁶ (64)  = 23,0,4 =2304

32² = 3² / 3x2x2 / 2²   =  10  / 2¹  (12)/ 4   = 10,2,4 = 1024

88² = 8² / 8x8x2 / 8²  = 77 / 4¹³   (134)/ 4⁶ (64)   = 77,4,4 =7744

Square of three digit numbers 

• first 2 digits square / first 2 digit x ones digit x 2 / ones digit square

123² = 12² / 12 x 3 x 2 / 3²   =  144 / 2⁷  (72)/ 9   = 151,2,9 =15129

453² = 45² / 45 x 3 x 2 / 3²   =  2052 / 0²⁷  (270)/ 9   = 2052,0,9 =205209

225² = 22² / 22 x 5 x 2 / 5²   =  506 / 2²²  (222)/ 5²   = 506,2,5 = 50,625

524² = 52² / 52 x 4 x 2 / 4²   =  2745 / 7⁴¹  (741)/ 6¹   = 274576 = 274576

324² = 32² / 32 x 4 x 2 / 4²   =  1049 / 7²⁵  (257)/ 6¹   = 1049,7,6 = 104976