Shortcuts On Squaring Two-digit Number Part Two
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Shortcuts on Squaring A 2-digit Number Part Two
Squaring A 2-digit Number Ending in 4
Sample Problem Number One : Find the Square of 54
Step One : Square 4
4 X 4 = 16
The last digit is 6 keep carry 1
_ _ _ 6
Step Two : Multiply the number in the tens digit which is 5 by 8 and add the carry 1.
5 X 8 = 40
40 + 1 = 41
The second digit in the product will be the next to the last digit in the square. Keep
The carry 4.
__ __ 1 6
Step Three : Square the first digit and add the carry.
5 X 5 = 25
25 + 4 = 29
The first two digits of the answer is 29
Therefore 54 X 54 = 2916
Example Two : Square 74
Step One : 4 X 4 = 16
__ __ __ 6
Keep the carry 1
Step Two : 7 X 8 = 56
56 + 1 = 57
__ __ 7 6
Keep the carry 5
Step Three : 7 X 7 = 49
49 + 5 = 54
Therefore 74 X 74 = 5476
Squaring A 2-digit Number Ending in 5
Sample Problem Number One : Find the Square of 45
Step One : The product of the number in the tens digit (4) and the number next to it (5) comprises
the first two digits in the square
4 X 5 = 20
2 0 __ __
Step Two : The last part of the answer is always 25
Therefore 45 X 45 = 2025
Example Two : Square 75
7 X 8 = 56
75 X 75 = 5625
Example Three : Square 55
5 X 6 = 30
55 X 55 = 3025
Squaring A 2-digit Number Ending in 6
Sample Problem Number One : Square 56
Step One : Square the number in the ones digit (6 ) and keep the carry.
6 X 6 = 36 keep the carry 3
The last digit of the answer is always 6.
__ __ __ 6
Step Two : Multiply the number in the tens digit by 2 and add the carry. Keep any carry.
5 X 2 = 10
10 + 3 = 13
The next digit of the answer is 3 keep the carry 1.
__ __ 36
Step Three : Multiply the number in the tens digit (5 ) by the next consecutive number and add the carry. The resulting answer comprises the first two digits in the square.
5 X 6 = 30
30 + 1 = 31
Therefore 56 X 56 = 3136
Example Two : Find the square of 86
Step One : 6 X 6 = 36
__ __ __ 6 keep carry 3
Step Two : 8 X 12 = 16
16 + 3 = 19 keep carry 1
The next digit of the answer is 9.
__ ___ 96
Step Three : 8 X 9 = 72
72 + 1 = 73
Therefore 86 X 86 = 7396
Practice Exercise
Try to Square the following numbers:
1) 84
2) 64
3) 44
4) 65
5) 85
6) 95
7) 76
8) 66
9) 46
Answers
1) 7056
2) 4096
3) 1936
4) 4225
5) 7225
6) 9025
7) 5776
8) 4356
9) 2116
SOURCE : MATH POWER By Divina Gracia T. Bandong
Shortcuts on Squaring A 2-digit Number Part Two
Squaring A 2-digit Number Ending in 4
Sample Problem Number One : Find the Square of 54
Step One : Square 4
4 X 4 = 16
The last digit is 6 keep carry 1
_ _ _ 6
Step Two : Multiply the number in the tens digit which is 5 by 8 and add the carry 1.
5 X 8 = 40
40 + 1 = 41
The second digit in the product will be the next to the last digit in the square. Keep
The carry 4.
__ __ 1 6
Step Three : Square the first digit and add the carry.
5 X 5 = 25
25 + 4 = 29
The first two digits of the answer is 29
Therefore 54 X 54 = 2916
Example Two : Square 74
Step One : 4 X 4 = 16
__ __ __ 6
Keep the carry 1
Step Two : 7 X 8 = 56
56 + 1 = 57
__ __ 7 6
Keep the carry 5
Step Three : 7 X 7 = 49
49 + 5 = 54
Therefore 74 X 74 = 5476
Squaring A 2-digit Number Ending in 5
Sample Problem Number One : Find the Square of 45
Step One : The product of the number in the tens digit (4) and the number next to it (5) comprises
the first two digits in the square
4 X 5 = 20
2 0 __ __
Step Two : The last part of the answer is always 25
Therefore 45 X 45 = 2025
Example Two : Square 75
7 X 8 = 56
75 X 75 = 5625
Example Three : Square 55
5 X 6 = 30
55 X 55 = 3025
Squaring A 2-digit Number Ending in 6
Sample Problem Number One : Square 56
Step One : Square the number in the ones digit (6 ) and keep the carry.
6 X 6 = 36 keep the carry 3
The last digit of the answer is always 6.
__ __ __ 6
Step Two : Multiply the number in the tens digit by 2 and add the carry. Keep any carry.
5 X 2 = 10
10 + 3 = 13
The next digit of the answer is 3 keep the carry 1.
__ __ 36
Step Three : Multiply the number in the tens digit (5 ) by the next consecutive number and add the carry. The resulting answer comprises the first two digits in the square.
5 X 6 = 30
30 + 1 = 31
Therefore 56 X 56 = 3136
Example Two : Find the square of 86
Step One : 6 X 6 = 36
__ __ __ 6 keep carry 3
Step Two : 8 X 12 = 16
16 + 3 = 19 keep carry 1
The next digit of the answer is 9.
__ ___ 96
Step Three : 8 X 9 = 72
72 + 1 = 73
Therefore 86 X 86 = 7396
Practice Exercise
Try to Square the following numbers:
1) 84
2) 64
3) 44
4) 65
5) 85
6) 95
7) 76
8) 66
9) 46
Answers
1) 7056
2) 4096
3) 1936
4) 4225
5) 7225
6) 9025
7) 5776
8) 4356
9) 2116
SOURCE : MATH POWER By Divina Gracia T. Bandong
Shortcuts on Squaring A 2-digit Number Part Two
Squaring A 2-digit Number Ending in 4
Sample Problem Number One : Find the Square of 54
Step One : Square 4
4 X 4 = 16
The last digit is 6 keep carry 1
_ _ _ 6
Step Two : Multiply the number in the tens digit which is 5 by 8 and add the carry 1.
5 X 8 = 40
40 + 1 = 41
The second digit in the product will be the next to the last digit in the square. Keep
The carry 4.
__ __ 1 6
Step Three : Square the first digit and add the carry.
5 X 5 = 25
25 + 4 = 29
The first two digits of the answer is 29
Therefore 54 X 54 = 2916
Example Two : Square 74
Step One : 4 X 4 = 16
__ __ __ 6
Keep the carry 1
Step Two : 7 X 8 = 56
56 + 1 = 57
__ __ 7 6
Keep the carry 5
Step Three : 7 X 7 = 49
49 + 5 = 54
Therefore 74 X 74 = 5476
Squaring A 2-digit Number Ending in 5
Sample Problem Number One : Find the Square of 45
Step One : The product of the number in the tens digit (4) and the number next to it (5) comprises
the first two digits in the square
4 X 5 = 20
2 0 __ __
Step Two : The last part of the answer is always 25
Therefore 45 X 45 = 2025
Example Two : Square 75
7 X 8 = 56
75 X 75 = 5625
Example Three : Square 55
5 X 6 = 30
55 X 55 = 3025
Squaring A 2-digit Number Ending in 6
Sample Problem Number One : Square 56
Step One : Square the number in the ones digit (6 ) and keep the carry.
6 X 6 = 36 keep the carry 3
The last digit of the answer is always 6.
__ __ __ 6
Step Two : Multiply the number in the tens digit by 2 and add the carry. Keep any carry.
5 X 2 = 10
10 + 3 = 13
The next digit of the answer is 3 keep the carry 1.
__ __ 36
Step Three : Multiply the number in the tens digit (5 ) by the next consecutive number and add the carry. The resulting answer comprises the first two digits in the square.
5 X 6 = 30
30 + 1 = 31
Therefore 56 X 56 = 3136
Example Two : Find the square of 86
Step One : 6 X 6 = 36
__ __ __ 6 keep carry 3
Step Two : 8 X 12 = 16
16 + 3 = 19 keep carry 1
The next digit of the answer is 9.
__ ___ 96
Step Three : 8 X 9 = 72
72 + 1 = 73
Therefore 86 X 86 = 7396
Practice Exercise
Try to Square the following numbers:
1) 84
2) 64
3) 44
4) 65
5) 85
6) 95
7) 76
8) 66
9) 46
Answers
1) 7056
2) 4096
3) 1936
4) 4225
5) 7225
6) 9025
7) 5776
8) 4356
9) 2116
SOURCE : MATH POWER By Divina Gracia T. Bandong
Shortcuts on Squaring A 2-digit Number Part Two
Squaring A 2-digit Number Ending in 4
Sample Problem Number One : Find the Square of 54
Step One : Square 4
4 X 4 = 16
The last digit is 6 keep carry 1
_ _ _ 6
Step Two : Multiply the number in the tens digit which is 5 by 8 and add the carry 1.
5 X 8 = 40
40 + 1 = 41
The second digit in the product will be the next to the last digit in the square. Keep
The carry 4.
__ __ 1 6
Step Three : Square the first digit and add the carry.
5 X 5 = 25
25 + 4 = 29
The first two digits of the answer is 29
Therefore 54 X 54 = 2916
Example Two : Square 74
Step One : 4 X 4 = 16
__ __ __ 6
Keep the carry 1
Step Two : 7 X 8 = 56
56 + 1 = 57
__ __ 7 6
Keep the carry 5
Step Three : 7 X 7 = 49
49 + 5 = 54
Therefore 74 X 74 = 5476
Squaring A 2-digit Number Ending in 5
Sample Problem Number One : Find the Square of 45
Step One : The product of the number in the tens digit (4) and the number next to it (5) comprises
the first two digits in the square
4 X 5 = 20
2 0 __ __
Step Two : The last part of the answer is always 25
Therefore 45 X 45 = 2025
Example Two : Square 75
7 X 8 = 56
75 X 75 = 5625
Example Three : Square 55
5 X 6 = 30
55 X 55 = 3025
Squaring A 2-digit Number Ending in 6
Sample Problem Number One : Square 56
Step One : Square the number in the ones digit (6 ) and keep the carry.
6 X 6 = 36 keep the carry 3
The last digit of the answer is always 6.
__ __ __ 6
Step Two : Multiply the number in the tens digit by 2 and add the carry. Keep any carry.
5 X 2 = 10
10 + 3 = 13
The next digit of the answer is 3 keep the carry 1.
__ __ 36
Step Three : Multiply the number in the tens digit (5 ) by the next consecutive number and add the carry. The resulting answer comprises the first two digits in the square.
5 X 6 = 30
30 + 1 = 31
Therefore 56 X 56 = 3136
Example Two : Find the square of 86
Step One : 6 X 6 = 36
__ __ __ 6 keep carry 3
Step Two : 8 X 12 = 16
16 + 3 = 19 keep carry 1
The next digit of the answer is 9.
__ ___ 96
Step Three : 8 X 9 = 72
72 + 1 = 73
Therefore 86 X 86 = 7396
Practice Exercise
Try to Square the following numbers:
1) 84
2) 64
3) 44
4) 65
5) 85
6) 95
7) 76
8) 66
9) 46
Answers
1) 7056
2) 4096
3) 1936
4) 4225
5) 7225
6) 9025
7) 5776
8) 4356
9) 2116
SOURCE : MATH POWER By Divina Gracia T. Bandong
Shortcuts on Squaring A 2-digit Number Part Two
Squaring A 2-digit Number Ending in 4
Sample Problem Number One : Find the Square of 54
Step One : Square 4
4 X 4 = 16
The last digit is 6 keep carry 1
_ _ _ 6
Step Two : Multiply the number in the tens digit which is 5 by 8 and add the carry 1.
5 X 8 = 40
40 + 1 = 41
The second digit in the product will be the next to the last digit in the square. Keep
The carry 4.
__ __ 1 6
Step Three : Square the first digit and add the carry.
5 X 5 = 25
25 + 4 = 29
The first two digits of the answer is 29
Therefore 54 X 54 = 2916
Example Two : Square 74
Step One : 4 X 4 = 16
__ __ __ 6
Keep the carry 1
Step Two : 7 X 8 = 56
56 + 1 = 57
__ __ 7 6
Keep the carry 5
Step Three : 7 X 7 = 49
49 + 5 = 54
Therefore 74 X 74 = 5476
Squaring A 2-digit Number Ending in 5
Sample Problem Number One : Find the Square of 45
Step One : The product of the number in the tens digit (4) and the number next to it (5) comprises
the first two digits in the square
4 X 5 = 20
2 0 __ __
Step Two : The last part of the answer is always 25
Therefore 45 X 45 = 2025
Example Two : Square 75
7 X 8 = 56
75 X 75 = 5625
Example Three : Square 55
5 X 6 = 30
55 X 55 = 3025
Squaring A 2-digit Number Ending in 6
Sample Problem Number One : Square 56
Step One : Square the number in the ones digit (6 ) and keep the carry.
6 X 6 = 36 keep the carry 3
The last digit of the answer is always 6.
__ __ __ 6
Step Two : Multiply the number in the tens digit by 2 and add the carry. Keep any carry.
5 X 2 = 10
10 + 3 = 13
The next digit of the answer is 3 keep the carry 1.
__ __ 36
Step Three : Multiply the number in the tens digit (5 ) by the next consecutive number and add the carry. The resulting answer comprises the first two digits in the square.
5 X 6 = 30
30 + 1 = 31
Therefore 56 X 56 = 3136
Example Two : Find the square of 86
Step One : 6 X 6 = 36
__ __ __ 6 keep carry 3
Step Two : 8 X 12 = 16
16 + 3 = 19 keep carry 1
The next digit of the answer is 9.
__ ___ 96
Step Three : 8 X 9 = 72
72 + 1 = 73
Therefore 86 X 86 = 7396
Practice Exercise
Try to Square the following numbers:
1) 84
2) 64
3) 44
4) 65
5) 85
6) 95
7) 76
8) 66
9) 46
Answers
1) 7056
2) 4096
3) 1936
4) 4225
5) 7225
6) 9025
7) 5776
8) 4356
9) 2116
SOURCE : MATH POWER By Divina Gracia T. Bandong
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