An intelligent way of squaring numbers using an algebraic identity given by ancient Indian mathematician Bhaskaracharya-II (1114-1193 CE). Learn this technique to do squaring mentally. Teachers can use this technique to teach mental squaring.

1. Squaring – 4
(from Bhaskara’s Lilavati)
Vinay Nair
SCHOOL OF VEDIC MATHS

2. • a2 – b2 = (a + b)(a – b)
• a2 = (a + b)(a – b) + b2

3. a2 = (a + b)(a – b) + b2
(i) 462 = (46 + 4)(46 – 4) + 42
= 50 x 42 + 16
=
2100
+ 16
=
2116
(ii) 582 = (58 + 8)(58 – 8) + 82
=
66 x 50 + 64
=
3300
+ 64
=
3364

4. a2 = (a + b)(a – b) + b2
(iii) 382 = (38 + 2)(38 – 2) + 22
= 40 x 36
+4
=
1440
+4
=
1444
(iv) 272 = (27 + 3)(27 – 3) + 32
= 30 x 24 + 9
=
720
+9
=
729

5. a2 = (a + b)(a – b) + b2
(v) 932 = (93 + 7)(93 – 7) + 72
= 100 x 86 + 49
=
8600
+ 49
=
8649
(vi) 892 = (89 + 11)(89 – 11) + 112
=
100 x 78
+ 121
=
7800
+ 121
=
7921

6. Thank you!