Squaring a 2-digit number ending in 8

1. Choose a 2-digit number ending in 8.
2. The last digit of the answer is always 4: _ _ _ 4
3. Multiply the first digit by 6 and add 6 (keep the
   carry): _ _ X _
4. Multiply the first digit by the next consecutive
   number and add the carry: the product is the first
   two digits: XX _ _.

Example:

1. If the number is 78:
2. The last digit of the answer is 4: _ _ _ 4
3. Multiply the first digit (7) by 6 and add 6 (keep the
   carry): 7 × 6 = 42, 42 + 6 = 48; the next digit of the
   answer is 8 (keep carry 4): _ _ 8 4
4. Multiply the first digit (7) by the next number (8)
   and add the carry (4):
   7 × 8 = 56, 56 + 4 = 60 (the first two digits): 6 0 _ _
5. So 78 × 78 = 6084.

See the pattern?

1. For 38 × 38
2. The last digit of the answer is 4: _ _ _ 4
3. Multiply the first digit (3) by 6 and add 6 (keep the
   carry): 3 × 6 = 18, 18 + 6 = 24; the next digit of the
   answer is 4 (keep carry 2): _ _ 4 4
4. Multiply the first digit (3) by the next number (4)
   and add the carry (2):
   3 × 4 = 12, 12 + 2 = 14 (the first two digits): 1 4 _ _
5. So 38 × 38 = 1444

Learn the pattern, practice other examples, and you will be a whiz at giving these squares.

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Squaring a 2-digit number ending in 7

1. Choose a 2-digit number ending in 7.
2. The last digit of the answer is always 9: _ _ _ 9
3. Multiply the first digit by 4 and add 4
   (keep the carry): _ _ X _
4. Multiply the first digit by the next consecutive number and
   add the carry: the product is the first two digits:
   XX _ _.

Example:

1. If the number is 47:
2. The last digit of the answer is 9: _ _ _ 9
3. Multiply the first digit (4) by 4 and add 4
   (keep the carry): 4 × 4 = 16, 16 + 4 = 20; the next
   digit of the answer is 0 (keep carry 2): _ _ 0 9
4. Multiply the first digit (4) by the next number (5)
   and add the carry (2):
   4 × 5 = 20, 20 + 2 = 22 (the first two digits): 2 2 _ _
5. So 47 × 47 = 2209.

See the pattern?

1. For 67 × 67
2. The last digit of the answer is 9: _ _ _ 9
3. Multiply the first digit (6) by 4 and add 4 (keep the
   carry): 4 × 6 = 24, 24 + 4 = 28; the next digit of the
   answer is 0 (keep carry 2): _ _ 8 9
4. Multiply the first digit (6) by the next number (7)
   and add the carry (2):
   6 × 7 = 42, 42 + 2 = 44 (the first two digits): 4 4 _ _
5. So 67 × 67 = 4489.
   

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Squaring a 2-digit number ending in 6

1. Choose a 2-digit number ending in 6.
2. Square the second digit (keep the carry): the last digit
   of the answer is always 6: _ _ _ 6
3. Multiply the first digit by 2 and add the carry
   (keep the carry): _ _ X _
4. Multiply the first digit by the next consecutive number and
   add the carry: the product is the first two digits:
   XX _ _.

Example:

1. If the number is 46, square the second digit :
   6 × 6 = 36; the last digit of the answer is 6
   (keep carry 3): _ _ _ 6
2. Multiply the first digit (4) by 2 and add the carry
   (keep the carry): 2 × 4 = 8, 8 + 3 = 11; the next digit
   of the answer is 1: _ _ 1 6
3. Multiply the first digit (4) by the next number (5)
   and add the carry: 4 × 5 = 20, 20 + 1 = 21
   (the first two digits): 2 1 _ _
4. So 46 × 46 = 2116.

See the pattern?

1. For 76 × 76, square 6 and keep the carry (3):
   6 × 6 = 36; the last digit of the answer is 6: _ _ _ 6
2. Multiply the first digit (7) by 2 and add the carry:
   2 × 7 = 14, 14 + 3 = 17; the next digit of the answer
   is 7 (keep carry 1): _ _ 7 6
3. Multiply the first digit (7) by the next number (8)
   and add the carry: 7 × 8 = 56, 56 + 1 = 57
   (the first two digits: 5 7 _ _
4. So 76 × 76 = 5776.
   

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Squaring a 2-digit number ending in 5

1. Choose a 2-digit number ending in 5.
2. Multiply the first digit by the next consecutive number.
3. The product is the first two digits: XX _ _.
4. The last part of the answer is always 25: _ _ 2 5.

Example:

1. If the number is 35, 3 × 4 = 12 (first digit
   times next number). 1 2 _ _
2. The last part of the answer is always 25: _ _ 2 5.
3. So 35 × 35 = 1225.

See the pattern?

1. For 65 × 65, 6 × 7 = 42 (first digit
   times next number): 4 2 _ _.
2. The last part of the answer is always 25: _ _ 2 5.
3. So 65 × 65 = 4225.

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Squaring a 2-digit number ending in 5

1. Choose a 2-digit number ending in 5.
2. Multiply the first digit by the next consecutive number.
3. The product is the first two digits: XX _ _.
4. The last part of the answer is always 25: _ _ 2 5.

Example:

1. If the number is 35, 3 × 4 = 12 (first digit
   times next number). 1 2 _ _
2. The last part of the answer is always 25: _ _ 2 5.
3. So 35 × 35 = 1225.

See the pattern?

1. For 65 × 65, 6 × 7 = 42 (first digit
   times next number): 4 2 _ _.
2. The last part of the answer is always 25: _ _ 2 5.
3. So 65 × 65 = 4225.

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Squaring a 2-digit number ending in 4

1. Take a 2-digit number ending in 4.
2. Square the 4; the last digit is 6: _ _ _ 6
   (keep carry, 1.)
3. Multiply the first digit by 8 and add the carry (1);
   the 2nd number will be the next to the last digit:
   _ _ X 6 (keep carry).
4. Square the first digit and add the carry: X X _ _.

Example:

1. If the number is 34, 4 × 4 = 16 (keep carry, 1);
   the last digit is _ _ _ 6.
2. 8 × 3 = 24 (multiply the first digit by 8), 24 + 1 = 25
   (add the carry):
   the next digit is 5: _ _ 5 6. (Keep carry, 2.)
3. Square the first digit and add the carry, 2: 1 1 5 6.
4. So 34 × 34 = 1156.

See the pattern?

1. For 84 × 84, 4 × 4 = 16 (keep carry, 1);
   the last digit is _ _ _ 6.
2. 8 × 8 = 64 (multiply the first digit by 8),
   64 + 1 = 65 (add the carry):
   the next digit is 5: _ _ 5 6. (Keep carry, 6.)
3. Square the first digit and add the carry, 6: 7 0 5 6.
4. So 84 × 84 = 7056.

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Squaring a 2-digit number ending in 3

1. Take a 2-digit number ending in 3.
2. The last digit will be _ _ _ 9.
3. Multiply the first digit by 6: the 2nd number will be
   the next to the last digit: _ _ X 9.
4. Square the first digit and add the number carried from
   the previous step: X X _ _.

Example:

1. If the number is 43, the last digit is _ _ _ 9.
2. 6 × 4 = 24 (six times the first digit): _ _ 4 9.
3. 4 × 4 = 16 (square the first digit), 16 + 2 = 18
   (add carry): 1 8 4 9.
4. So 43 × 43 = 1849.

See the pattern?

1. For 83 × 83, the last digit is _ _ _ 9.
2. 6 × 8 = 48 (six times the first digit): _ _ 8 9.
3. 8 × 8 = 64 (square the first digit), 64 + 4 = 68
   (add carry): 6 8 8 9.
4. So 83 × 83 = 6889.

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Squaring a 2-digit number ending in 2

1. Take a 2-digit number ending in 2.
2. The last digit will be _ _ _ 4.
3. Multiply the first digit by 4: the 2nd number will be
   the next to the last digit: _ _ X 4.
4. Square the first digit and add the number carried from
   the previous step: X X _ _.

Example:

1. If the number is 52, the last digit is _ _ _ 4.
2. 4 × 5 = 20 (four times the first digit): _ _ 0 4.
3. 5 × 5 = 25 (square the first digit), 25 + 2 = 27 (add carry): 2 7 0 4.
4. So 52 × 52 = 2704.

See the pattern?

1. For 82 × 82, the last digit is _ _ _ 4.
2. 4 × 8 = 32 (four times the first digit): _ _ 2 4.
3. 8 × 8 = 64 (square the first digit), 64 + 3 = 67 (add carry): 6 7 2 4.
4. So 82 × 82 = 6724.

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Squaring a 2-digit number ending in 1

1. Take a 2-digit number ending in 1.
2. Subtract 1 from the number.
3. Square the difference.
4. Add the difference twice to its square.
5. Add 1.

Example:

1. If the number is 41, subtract 1: 41 - 1 = 40.
2. 40 × 40 = 1600 (square the difference).
3. 1600 + 40 + 40 = 1680 (add the difference twice
   to its square).
4. 1680 + 1 = 1681 (add 1).
5. So 41 × 41 = 1681.

See the pattern?

1. For 71 × 71, subtract 1: 71 - 1 = 70.
2. 70 × 70 = 4900 (square the difference).
3. 4900 + 70 + 70 = 5040 (add the difference twice
   to its square).
4. 5040 + 1 = 5041 (add 1).
5. So 71 × 71 = 5041.

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Squaring a 2-digit number beginning with 9

1. Take a 2-digit number beginning with 9.
2. Subtract it from 100.
3. Subtract the difference from the original number:
   this is the first part of the answer.
4. Square the difference: this is the last part of the answer.

Example:

1. If the number is 96, subtract: 100 - 96 = 4, 96 - 4 = 92.
2. The first part of the answer is 92 _ _ .
3. Take the first difference (4) and square it: 4 × 4 = 16.
4. The last part of the answer is _ _ 16.
5. So 96 × 96 = 9216.

See the pattern?

1. For 98 × 98, subtract: 100 - 98 = 2, 98 - 2 = 96.
2. The first part of the answer is 96 _ _.
3. Take the first difference (2) and square it: 2 × 2 = 4.
4. The last part of the answer is _ _ 04.
5. So 98 × 98 = 9604.

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Squaring a 2-digit number beginning with 1

1. Take a 2-digit number beginning with 1.
2. Square the second digit
   (keep the carry) _ _ X
3. Multiply the second digit by 2 and
   add the carry (keep the carry) _ X _
4. The first digit is one
   (plus the carry) X _ _

Example:

1. If the number is 16, square the second digit:
   6 × 6 = 36 _ _ 6
2. Multiply the second digit by 2 and
   add the carry: 2 × 6 + 3 = 15 _ 5 _
3. The first digit is one plus the carry:
   1 + 1 = 2 2 _ _
4. So 16 × 16 = 256.

See the pattern?

1. For 19 × 19, square the second digit:
   9 × 9 = 81 _ _ 1
2. Multiply the second digit by 2 and
   add the carry: 2 × 9 + 8 = 26 _ 6 _
3. The first digit is one plus the carry:
   1 + 2 = 3 3 _ _
4. So 19 × 19 = 361.

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