# Shortcuts On Squaring Two-digit Numbers Part Three

**SHORTCUTS ON SQUARING 2-DIGIT NUMBERS**

**PART THREE**

__Squaring 2-digit number ending in 7.__

__Problem Number One: Square 57__

**Step One: **If the number is 57, the last digit of the square is 9.

**_ _ _** 9

**Step Two: **Multiply the first digit by 4 and add 4. The last digit of the result comprises the next to the last digit in the square (keep any carry)

5 x 4 = 20

20 + 4 = 24

The next digit of the answer on the right is 4 (keep carry 2)

_ _ _ 49

**Step Three: **Multiply by the first digit by the number next to it and add any carry. The result becomes the first part of the answer:

5 x 6 = 30

30 + 2 = 32

first two digits : 32

3249

Therefore 57 x 57 = 3249

__Problem Number Two: Square 67__

**Step One:** _ _ _ 9

**Step Two: **6 x 4 = 24

24 x 4 = 28

_ _ _ 89

**Step Three: **

6 x 7 = 42

42 + 2 = 44

__ 4489

Therefore 67 x 67 = 4489

__Squaring a 2-digit number ending in 8.__

__Probleem Number One:__

**Square 58**

**Step One: **The last digit of the answer is always 4.

**_ _ _ 4**

**Step Two: **Multiply the first digit by 6 and add 6. Keep any carry.

5 x 6 = 30

30 + 6 = 36

The next digit of the answer is 6 (keep carry 3)

_ _ _ 64

**Step Three**: Multiply the first digit by the next consecutive number and add the carry. The result comprises the first two digits in the square:

5 x 6 = 30

30 + 3 = 33

First two digits of the answer is 33.

Therefore 58 x 58 = 3364

**Problem Number Two **

**Square 68:**

**Step One: _ _ _ 4**

**Step Two: **6 x 6 = 36

36 + 6 = 42

_ _ _ 24

**Step Three**: 6 x 7 = 42

42 + 4 = 46

Therefore: 68 x 68 = 4624

__Squaring a 2-digit number ending in 9.__

**Problem Number One:**

**Square 69:**

**Step One**. The last digit is always 1:

**_ _ _ 1**

**Step Two: **Multiply the first digit by and add 8. Keep any carry.

6 x 8 = 48

48 + 8 = 56

The next digit of the answer is 6. (Keep carry 5):

_ _ _ 61

**Step Three**: Multiply the first digit by the next consecutive number and add the carry. The result comprises the first two digits in the square:

6 x 7 = 42

42 + 5 = 47

The first two digits of the answer is 47.

Therefore 69 x 69 = 4761

**SamSample Problem two:**

**Square 79.**

**Step One: **_ _ _ 1

7 x 8 = 56

56 + 8 = 64

_ _ _ 41

**Step Three**: 7 x 8 = 56

56 + 6 = 62

Therefore: 79 x 79 = 6241

**PRAPPRATICE EXERCISES:**

Try to Square the following numbers: ANSWERS:

1. 87 (1) 7569

2. 77 (2) 5929

3. 97 (3) 9409

4. 78 (4) 6084

5. 88 (5) 7744

6. 98 (6) 9604

7. 59 (7) 3481

8. 49 (8) 2401

9. 39 (9) 1521

SOURCE: MATH POWER

By: Divina Gracia T. Bandong