Question

What is the smallest number that must be added to 4515600 to get a perfect square?

Answer 1

Hint: Try to find the square root of 4515600 and then see the closest number that can be the perfect square and at last find the square of the closest number and subtract it with the number given to us.

Complete step-by-step solution:
So we are given the number 4515600
If we try to find \[\sqrt {4515600} = {\rm{2,124}}{\rm{.994117638917}}\]
Now we can see that
\[\begin{array}{l}
 \Rightarrow {(2124)^2} < 4515600\\
 \Rightarrow {(2125)^2} > 4515600
\end{array}\]
Clearly 2125 is the closest square which is greater than the given number so if we try to find the square of 2125 it will come out as \[4515625\] then if we subtract the numbers it will be
\[4515625 - 4515600 = 25\]
So the least number to be added to the given number which can give us a perfect square is 25.

Note: We can also do this problem by another approach, i.e., if we try to find the square root of 4515600 using the long division method in last we will get the remainder as 25 which won't be further divisible by any so that means that if we add 25 to the given number we can easily get the required perfect square.