Take any number ending in 5. (for example 35). Multpily the first part of the number (3) by the next higher number (4) and then add 25 to the end. (to give you 1225) That's what 35 to the power of two is equal to. This works for any number that ends in five. explain why this works
thanks! :)
let the number without the ending 5 be x
so our number is 10x+5 , (to add 5 would mean the x has to shift one over, or is multiplied by 10.)
e.g. I was thinking of 135 , so x = 13
and 10x+5 = 130+5 = 135
so the number squared is
(10x+5)^2 = 100x^2 + 100x + 25
short cut involves multiplying x(x+1) which gives us
x^2 + x
now we are supposed to add 25 to the end of this, which means we add two place holder values
that involves multiplying what we have by 100
so our final result is 100(x^2+x) + 25
or 100x^2 + 100x + 25
e.g.
135^2 = 18225
short way: our x= 13
so x(x+1) = 13(14) = 182
but by adding 25 to the end of the sequence, the 182 becomes 100(182) = 18200
adding 25 now gives us the necessary 18225