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Shortcuts On Squaring Two-digit Number Part Two

Updated on October 23, 2009

 

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  

 

  

  

 

 

 

 

 

 

 

                          

 

 

                               

 

 

 

      

 

 

                               

Comments

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    • Caleb DRC profile image

      Caleb DRC 

      6 years ago

      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.

    • profile image

      JDL 

      7 years 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.

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