3prove that the last decimal digit of a perfect square cannot be 2, 3, 7 or 8.
post different methods to find if 22051946 is a perfect square . at least 5 shorter methods
-
UP 0 DOWN 0 0 5
5 Answers
621) not a multiple of 4.. hence not perfect square..
2) Deterministic.. try to find the actual value of the square root
49nishant bhaiy's post is correct if any EVEN number is a perfect square it must be a multiple of 4 else it must be odd!!
49as per minch's post...
r an be even that is r=2n
then 4q+r=4q+2n=2(2q+n)
(4q+r)2=4(2q+n)2=4m
or r can be odd that r=2n+1
then 4q+r=4q+2n+1=2(2q+n)+1=odd
(4q+r)2=4(2q+n)2+4(2q+n)+1=4m+1
3