Take-home question: Here are examples of a shortcut for mentally squaring a number.
Example 1) 76²: Go to the closest multiple of 10-here, for 76, plus 4 to 80. Then go the opposite way from 76 by the same amount, minus 4 to 72. Multiply 80 and 72 mentally for 5760. Add the square of the up-down number 4. As a result, 5760 + 16 = 5776 and 76² = 5776.
Example 2) 62²: Go to 60 (down 2). Then go up from 62 by 2 to 64. Therefore, 60 × 64 = 3840. Add the square of 2 for 62² = 3844.
Example 3) 57²: Go to 60 then 54. Therefore, 60 × 54 = 3240. Add 3² for 57² = 3249.
Example 4) 198²: 200 × 196 = 39,200. Add 2² for 39,204 (= 198²).
A) Use the shortcut to calculate 37² mentally, and then write the mental steps you did.
B) Give a justification that the method works for squaring any n. Label the up-down number x.

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The Answer of Take-home question: Here are examples of a shortcut for mentally squaring a number. Example 1) 76²: Go to the closest multiple of 10-here, for 76, plus 4 to 80. Then go the opposite way from 76 by the same amount, minus 4 to 72. Multiply 80 and 72 mentally for 5760. Add the square of the up-down number 4. As a result, 5760 + 16 = 5776 and 76² = 5776. Example 2) 62²: Go to 60 (down 2). Then go up from 62 by 2 to 64. Therefore, 60 × 64 = 3840. Add the square of 2 for 62² = 3844. Example 3) 57²: Go to 60 then 54. Therefore, 60 × 54 = 3240. Add 3² for 57² = 3249. Example 4) 198²: 200 × 196 = 39,200. Add 2² for 39,204 (= 198²). A) Use the shortcut to calculate 37² mentally, and then write the mental steps you did. B) Give a justification that the method works for squaring any n. Label the up-down number x.

Take-Home Question: Here Are Examples of a Shortcut for Mentally