Maths Tricks and Shortcuts Squaring Numbers near 1000

Mental Math with Tricks and Shortcuts

Squaring Numbers near 1000

Examples

a2 = [a – (1000 – a)]1000 + (1000 – a) 2 . 9942 = (994 – 6)1000 + 6 2 = 988036

a2 = [a + (a – 1000)]1000 + (a – 1000) 2 , 10072 = (1007 + 7)1000 + 72 = 1014049

Squaring Numbers that end in 1

a2 = (a – 1) 2 + 2a - 1 , 61 2 = 60 2 + 122 - 1 = 3600 + 121 = 3721

Squaring Numbers that end in 4

a2 = (a + 1)2 – (2a + 1) , 442 = 452 – (88 + 1) = 2025 - 89 = 1936

Squaring Numbers that end in 6

a2 = (a - 1)2 + (2a - 1) , 562 = 552 + 112 - 1 = 3025 + 111 = 3136

Squaring Numbers that end in 9

a2 = (a + 1) 2 – (2a + 1) , 792 = 802 – (158 + 1) = 6400 – 159 = 6341

Using Squares to Help Multiply

Two Numbers that Differ by 1

If a > b then a x b = a2 – a , 35 x 34 = 1225 – 35 = 1190

If a < b =" a2 + a, 35 x 36 = 1225 + 35 = 1260

Two Numbers that Differ by 2

Two Numbers that Differ by 3 (a <>

a x b = (a + 1)2 + (a – 1) , 26 x 29 = 272 + 25 = 729 + 25 = 754

a x b = [(a + b)/2]2 – 4 , 64 x 68 = 662 – 4 = 4356 - 4 = 4352

Two Numbers that Differ by 6

a x b = [(a + b)/2]2 – 9 , 51 x 57 = 542 – 9 = 2916 – 9 = 2907

Two Numbers that Differ by an Even Number: a < c =" (b">

a x b = [(a + b)/2]2 – c2 , 59 x 67 = 632 – 42 = 3969 – 16 = 3953