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# Squaring numbers in the 60s Square the last digit (keep the carry)   _ _ _ X Multiply the last digit by 12, add the carry   _ _ X _ The first digits will be 36 plus the carry:   X X _ _ Example: If the number to be squared is 63: Square the last digit (keep the carry): 3 × 3 = 9 (keep 3)     _ _ _ 9 Multiply the last digit by 12, add the carry: 12 × 3 = 36 (keep 3)    _ _ 6 _ The first digits will be 36 plus the carry: 36 (+ carry): 36 + 3 = 39    3 9 _ _ So 63 × 63 = 3969. See the pattern? If the number to be squared is 67: Square the last digit (keep the carry): 7 × 7 = 49 (keep 4)     _ _ _ 9 Multiply the last digit by 12, add the carry: 12 × 7 = 84, 84 + 4 = 88    _ _ 8 _ The first digits will be 36 plus the carry: 36 (+ carry): 36 + 8 = 44  4 4 _ _ So 67 × 67 = 4489. Sourabh Singh IIT Patna