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help!why!

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5*5*5*5*5*5*5=?

最佳解答:

since (10a+5)^2 = 100a^2 + 100a+25 = 100a(a+1) +25 y i do this ? example : 15 ^2 = 1 x (1 + 1) x 100 + 25 = 225 (15^2 means 15 x 15) 35^2 = 3 x (3 + 1)x 100 +25 = 1225 (35^2means 35 x 35) so 25 never change for the last two digit bcoz only a will change in this formula and after that just very simpe for a<11 for the second one i just do 3 x(3 +1) then is 12 and then i just put 25 behind = 1225 (try others if you don t believe) (remember this only works for the number which the last digit is 5 and only for square) now i can say 5 x 5 x 5 x 5 x 5 x 5 x 5 = 25 x 25 x 25 x 25 / 5 = 625 x 625 / 5 again i can do a formula : (100a+10b+c)^2 (10b+c = 25 here) =(100a +25 )^2 =10000a^2 +5000a+(25)^2 (we know that 25^2 = 625 from above) =10000a(a+0.5) +625 again you can see if there have something25 ^2 appear, the last three digit will not change, there,s always 625 so 425^2 = 10000(4 x 4.5 )+625 = 180625 ( 4 x 4.5 = 4 x 4 + 4 x 0.5 = 16 + 2 = 18 ) 525^2 = 10000(5 x 5.5 )+625 = 275625 (5 x 5.5 = 5 x 5 + 5 x 0.5 = 25+2.5 = 27.5) and 625^2 = 10000(6 x 6.5 ) +625 = 390625 and now i can write : 5 x 5 x 5 x 5 x 5 x 5 x 5 = 625 x 625 = 390625 / 5 =390625x 2 / 10 (1/ 5 = 2 / 10) =781250/ 10 =78125 all of the above i just using some shortcut otherwise you have to do 5 x 5 x 5 x 5 x 5 x 5 x 5 yourself or use caculator 2007-11-27 07:15:36 補充： anothershort cut :(10 +a )(10 + b)=100+10(a +b)+ab=10(10+a+b) +abtry this:11 x 12 = ( 11+2 )x 10 + 1 x 2 = 130 + 2 = 132 (11= 10 +a here , and b = 2 )19 x 18 = ( 19+8 )x 10 + 9 x 8 = 270 + 72 =342(this can only use between 10 and 19) 2007-11-27 07:22:38 補充： y i do this again?combie the first and the third formula , i can easy say (115x 115 ) = (115)^2 = 13225(185x 185 ) = (185)^2 = 34425if you are asking something like that, hope this will helpful, otherwise better use your caculator

其他解答:

5*5*5*5*5*5*5 =25*5*5*5*5*5 =125*5*5*5*5 =625*5*5*5 =3125*5*5 =15625*5 =78125|||||78125|||||=78125 ok?8758B59A7FA1EEA7