Question

How Many four digit numbers have 4 and 5 at their unit place

Answer 1

Answer:

21 no.s

Step-by-step explanation:

In case of 4-digit perfect squares,

Smallest  =1024=322  

Largest  =9801=992  

=> There are  (99−32+1)=68  4-digit perfect squares.

Now, we have to find how many of them have 4 , and 5 in their units place.

Case 1: 4 in Units place

Rule: If a number has 2 or 8 in the unit place, then its square has 4 in the units place

So, going by this logic, the possibilities are  32^2 ,  38^2 ,  42^2 ,  48^2 ,  52^2 ,  58^2 ,….,  92^2  and  98^2  

So, 14 such numbers

Case 2: 5 in units place

Rule: If a number has 5 in the unit place, then its square has 5 in the units place

Going by this logic, the possibilities are  35^2 ,  45^2 ,  55^2 , ….,  85^2  

So, 7 such numbers