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Maths Tricks of Squaring Numbers In The Four Hundreds 

Squaring numbers in the four hundreds 
Choose a number in the 400s (keep the numbers low at first; then progress to larger ones). The first two digits of the square are 16: 1 6 _ _ _ _ The next two digits will be 8 times the last 2 digits: _ _ X X _ _ The last two places will be the square of the last two digits: _ _ _ _ X X Example: If the number to be squared is 407: The first two digits are 16: 1 6 _ _ _ _ The next two digits are 8 times the last 2 digits: 8 x 7 = 56: _ _ 5 6 _ _ Square the last digit: 7 x 7 = 49: _ _ _ 4 9 So 407 x 407 = 165,649.
For larger numbers reverse the steps:
Square the last two digits (keep the carry): _ _ _ _ X X 8 times the last two digits + carry: _ _ X X _ _ 16 + carry: X X _ _ _ _
See the pattern?
If the number to be squared is 425: Square the last two digits (keep the carry): 25 x 25 = 625 (keep 6): _ _ _ _ 2 5 8 times the last two digits + carry: 8 x 25 = 200; 200 + 6 = 206 (keep 2): _ _ 0 6 _ _ 16 + carry: 16 + 2 = 18: 1 8 _ _ _ _ So 425 x 425 = 180,625.




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