Do the Math!!! Squaring Two-Digit Numbers

I was browsing the web last night when my classmate messaged me about a web site that gives excellent Math tips.

Perfect for those people who are having a hard time with Mathematics. (Like me. Hehe )

DISCLAIMER: I do not claim that I am the author of these tips, I just copied it for educational and entertainment purposes only. Also, I am in no way connected to B. Lee Clay, the author of Beatcalc.

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.

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.

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.

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.

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.

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.

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.

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.

Squaring a 2-digit number ending in 9

1. Choose a 2-digit number ending in 9.
2. The last digit of the answer is always 1: _ _ _ 1
3. Multiply the first digit by 8 and add 8 (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 39:
2. The last digit of the answer is 1: _ _ _ 1
3. Multiply the first digit (3) by 8 and add 8 (keep the carry): 8 × 3 = 24, 24 + 8 = 32; the next digit of the answer is 2 (keep carry 3): _ _ 2 1
4. Multiply the first digit (3) by the next number (4) and add the carry (3): 3 × 4 = 12, 12 + 3 = 15 (the first two digits): 1 5 _ _
5. So 39 × 39 = 1521.

Hey!
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