First we rewrite these numbers as fractions and simplify there denominators if possible.
#4.246 = 4246/1000 = 4246/10^3#
So #4.246 * 4.246 = 4246/10^3 * 4246/10^3# can be rewritten as #(4246 * 4264)/(10^3*10^3)#.
Two equal numbers set to a power can be multiplied by setting that same number to the power of the two original powers added together. #10^3 * 10^3 = 10^(3+3) = 10^6#.
So now we are left with: #(4246 * 4246) /10^6 #.
#4246 * 4246# can be rewritten as #(4000 + 200 + 40 + 6) * (4000 + 200 + 40 + 6)#.
Now we can solve using simple multiplication and addition:#((4000 + 200 + 40 + 6) * (4000 + 200 + 40 + 6)) /10^6#.
#((4000 + 200 + 40 + 6) * (4000 + 200 + 40 + 6)) /10^6#
#= ((4000 * 4000) + (4000 * 200) + (4000*40) + (4000*6) + (200 + 40 +6) * (4000 + 200 + 40 + 6))/10^6#.
#= (16984000 + (200 + 40 +6) * (4000 + 200 + 40 + 6))/10^6#
#= (16984000 + (200*4000) + (200*200) + (200*40) + (200*6) + (40 +6) * (4000 + 200 + 40 + 6))/10^6#
#= (16984000 + 849200 + (40 +6) * (4000 + 200 + 40 + 6))/10^6#
#= (16984000 + 849200 + (40*4000) + (40*200) + (40*40) + (40*6) + 6 * (4000 + 200 + 40 + 6))/10^6#
#= (16984000 + 849200 + 169840 + 6 * (4000 + 200 + 40 + 6))/10^6#
#= (16984000 + 849200 + 169840 + (6 * 4000) + (6 * 200) + (6*40) + (6*6))/10^6#
#= (16984000 + 849200 + 169840 + 25476)/10^6#
#= (18028516)/10^6#
Now the last step is to divided by 10^6 which is equal to adding 6 decimal places to a number.
#= (18028516)/10^6 = 18.028516#
