# 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.

## More by this Author

- 4
Solving Geometry Problems Involving System of Equations In Two Variables Algebra has also found wide applications in Geometry. Among its common problems are problems involving perimeters and angles. In this hub I...

- 6
SolvingWord Problems Involving Exponential Function Exponential function is one of the most important concept in Algebra. In this hub I present several problems involving exponential function with their...

- 4
Solving Word Problems Involving Chebyshev’s Theorem Chebyshev’s Theorem states that the proportion or percentage of any data set that lies within k standard deviation of the mean where k is any...

## 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