(*) Squaring A Number Ending In 5: A. Squaring a number ending in 5 is very easy. The method comes from algebra: (10 a + 5) 2 = 100 (a)(a + 1) + 25 B. Using numbers instead of variables we get the following: 1. Write down 25 . 2. Multiply the number in the ten’s digit by that number plus 1. Write this number down. Ex [1 ] 35 2 =_________. a) Write 25 . b) 3 x (3 + 1) = 3 x 4 = 12 c) The answer is 1225 Ex [2 ] 115 2 =_________. a) Think of 11 as being the number in the ten’s digit. b) Write 25 . c) 11 x (11 + 1) = 11 See Multiplying by 11 d) The answer is 13225
A. From algebra we can also use: (10 a – 4) 2 = 100 (a)(a-1) + 10(2 a + 1) + 6 B. Using numbers instead of variables we get the following: 1. Write down 6. 2. Add 1 to the ten’s digit, multiply by 2, then add 1. Write this number down. necessary. 3. Multiply the number in the ten’s digit by that number plus 1. Write this result. Ex [1 ] 66 2 =_________. a) Write down 6. b) 2 x (6 + 1) + 1 = 15 . Write 5, carry *1. c) 6 x (6 + 1) = 42 + *1 = 43 d) The answer is 4356 . Ex [2 ] 86 2 =_________. a) Write down 6. b) 2 x (8 + 1) + 1 = 19 . Write 9, carry *1. c) 8 x (8 + 1) = 72 + *1 = 73 d) The answer is 7396 .
(**) Squaring A Number Ending In 7: A. This method comes from algebra: (10 a – 3) 2 = 100 (a)(a - 1) + 10(4 a) + 9 B. Using numbers instead of variables we get the following: 1. Write down 9. 2. Add 1 to the ten’s digit and multiply by 4. Write this number down, carry if necessary. 3. Multiply the number in the ten’s digit by that number plus 1. Write this result. Ex [1 ] 37 2 =_________. a) Write down 9. b) 4 x (3 + 1) = 16 . Write 6, carry *1. c) 3 x (3 + 1) = 12 + *1 = 13 . d) The answer is 1369 . Ex [2 ] 87 2 =_________. a) Write down 9. b) 4 x (8 + 1) = 36 . Write 6, carry *3. c) 8 x (8 + 1) = 72 + *3 = 75 . d) The answer is 7569 .
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