Is there a shortcut to quickly find a square of a number? let's say 65 squared..

Question

jtvatsim · Answer

There are a lot of methods out there for "fast math tricks". If you Google "how to square numbers in your head" you will find a lot of info.

anonymous · Answer

Yes! (a + b)^2 = (a + b) x (a + b) = a^2 + 2ab + b^2 , where 60 is a ,and 5 is b. You can do this with any two digit number easily.

jtvatsim · Answer

Stole my idea @shawmoes ! :)
(65)^2 = (60 + 5)^2 = 60^2 + 2*60*5 + 5^2 = 3600 + 2*300 + 25 = 4225.

hartnn · Answer

the 2 digit numbers ending in 5 are special cases :)

15^2 = 225 
25^2 = 625 
35^2 = 1225 
45^2 = 2025
....
notice any pattern??

the last 2 digits are ALWAYS 25.
the first part of the answer is alsways 
$\large n 
\times (n+1)$

85^2 
$\Large 8\times 9 =72\
\\Large 85^2 = 7225$)

mathmath333 · Answer

there is a good book for quick mental math with vast ideas for multiplication, addition , substraction, division. , i have read that and i think it very useful http://en.wikipedia.org/wiki/Trachtenberg_system $\text{Trachtenberg system of speed mathmatics - Jakow Trachtenberg}$