# Shortcuts On Squaring Two-Digit Numbers Part One

SHORTCUTS ON SQUARING TWO-DIGIT NUMBERS Part One

A. Squaring 2-digit number ending in one

Example One : Square 51

Step One : Take a two-digit number ending in 1, then subtract 1 from it.

51 – 1 = 50

Step Two : Square the difference

50 * 50 = 2500

Step Three : Double the difference in step one 1 and add it to the square in step two

2500 + 100 = 2600

Step Four : Add 1 to the sum in step three

2600 + 1 = 2601

Therefore 51 * 51 = 2601

Example two : Square the number 71

Step one : 71 – 1 = 70

Step two : 70 * 70 = 4900

Step three : 4900 + 140 = 5040

Step four : 5040 + 1 = 5041

Therefore 71 * 71 = 5041

B. Squaring a 2-digit number ending in 2

Example One : Square 62

Step One : Take a two-digit number ending in 2. If the number is 62, the last digit in the square

is 4 . _ _ _ 4

Step two : Multiply the first digit by 4 =è 6 * 4 = 24

The second digit in the produc t will be the next to the last digit in the square. Keep any carry.

_ _ 4 4

Step three: Square the first digit and add the number carried from the previous step.

6 * 6 = 36

36 + 2 = 38

Threfore the square of 62 is 3844

Example two : Square 72

First step : 2 * 2 = 4

Second step : 7 * 4 = 28 =è _ _ 84

Third step : 7 * 7 = 49 ==è 49 + 2 = 51

Therefore 72 * 72 = 5184

C. Squaring a 2-digit number ending in 3.

Example one : Square 53

Step one : Take a two-digit number ending in 3. The last digit of the square will be 9.

Step two : Multiply the first digit by 6. The second digit in the product will be the next number to

The last digit in the square . Keep any carry.

5 * 6 = 30

_ _ 0 9

Step three : Square the first digit and add the number carried from the previous step .

5 * 5 = 25

25 + 3 = 28

Therefore 53 * 53 = 2809

Example two : Square 83

Step one : 3 * 3 = 9

Step two : 8 * 6 = 48

_ _ 8 9

Step three : 8 * 8 = 64

64 + 4 = 68

Therefore 83 * 83 = 6889

SOURCE : MATH POWER by Divina Gracia T. Bandong.

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## Comments 1 comment

Good one, useful one, but I think in CASE I, two digit number ending with one, it is easier if we use

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