Math Tricks!

Here are two sweet 'quick' Math tips. This was 'new learning' for me since I didn't know it, hence they find a place in this blog, even though they might be pretty well known, not sure.

1) This one I learnt today from my husband:
How can you quickly compute the square of any number ending with 5? For eg., 25*25, 65*65, or even 1035*1035?
Answer: The last 2 digits of the square will always be 25. The part that's more fascinating is this: to get the remaining digits, simply mutiply the number formed by all digits of the original number excluding the last digit (i.e. 5), with that number + 1. For example, for 65*65, the part of the number excluding last digit 5 is '6'. Mutiply 6 by (6+1) , that is, 6*7=42. Now pre-pend this number to 25, to get the result. So 65*65 = 4225. Similarly, 85*85 = (8*9) prepended to 25 i.e. 7225. And 1035*1035 = 1071225, which is (103*104) concatenated with 25.
Isn't that neat, and simple!

2) This one I came across in a book, and then quickly realized that it is actually a simple application of the square of (a +or- b), which is sqr(a) + (+or-) 2*a*b + sqr(b). Actually my dad has mentioned this trick to me way back when I was in middle school.
The question is to quickly calculate the square of numbers that are close to 50, for example, say 48. All you have to do is sqr(50) = 2500. Then calculate 50*2*(the difference of that number from 50) = 100*(difference of the number from 50). So in this case, we get 100*(50-48) = 200. Then, if the original number is greater than 50, add this result to 2500, else subtract this result from 2500. So in this case, 48 being lesser than 50, we subtract 200 from 2500 to get 2300. This (2300) is the approximate value of the square of 48. To get a precise value, add in the square of the difference of the original number from 50. So, in this case, we would add (to 2300), a value of sqr(50-48) = sqr(2) = 4. So the exact answer is 2300+4 = 2304.
Here's another one to illustrate, in case you got confused :-)
53*53 : We need 2500+ 100*(53-50) + 3*3 = 2500 + 300 + 9 = 2809.
Ain't it cool :-)