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
CommentsLoading...
Very fascinating, Cristina. I never knew this. Very professional a thorough job!
There is a really cool trick to get rid of huge spaces between your capsules. Go into edit mode---find capsule that is being a pain---put mouser at the lower left corner---start pushing "backspace" until all the space is taken up.
JDL 18 months ago
Your Shortcuts are not short whatsoever. There are MUCH quicker ways. This is the way I was taught in high school, the old fashioned slow way. Just use the 100 rule. Actually math is pretty cool because there are so many ways to do it, it is kind of fun computing the longest equation to reach a solution.