Question

What is the least number that should be added to 6200 to make it a perfect square?

Answer 1

Hint: We are going to use the nearest square number process to find the square that is required. We double check about it being greater than 6200. Then we use subtraction to find the number that’s to be added to 6200.

Complete step-by-step answer:
We need to find the number to be added to 6200.
So, we are going to find the closest possible square number less than 6200.
We can apply square theorem or long-division root to find it.
We get that $6200=62\times 100=62\times {{10}^{2}}$. So, we mostly look at the closest possible square number greater than 62.
The number is $8\times 8=64$. So, we take $80\times 80=6400$.
We changed the condition from less to greater as the number 6200 more closest toward the 80 rather than 70.
Now we need to turn back to reach near 6200.
So, we take 79 and we get a square $79\times 79=6241$. It’s very close to 6200.
We go 1 step more back and take 78.
Doing square we get $78\times 78=6084$. We went less than 6200.
So, the close square numbers to 6200 are 6084 and 6241.
We have been instructed to find the least number that should be added to 6200 to make it a perfect square.
If we are going to add numbers then we get greater than 6200.
So, the number we want is 6241 which is a square of 79.
So, the number to be added is $6241-6200=41$.
The least number is 41.

Note: We can also use a long-divisor root process to find out the number that’s to be added to 6200. The process we used is more like a trial and error method to find the closest possible square number greater than 6200.