Question

Find the least number which must be added to 6041 to get a perfect square.

Answer 1

It is clear that the given number 6041 is not a perfect square. Further, some number needs to be added to it to make it a perfect square.

Let us use the long division method for finding the square root of 6041 and let’s see what we get.

We get the quotient as 77.

Let us now find the square of 77 and its next number, that is, 78.
${77}^2$ = 77 $\times$ 77 = 5929
${78}^2$ = 78 $\times$ 78 = 6084

5929 < 6041 < 6084
It is obvious from above that 6084 is the perfect square closest to 6041.

6084 $-$ 6041 = 43

So we need to add 43 to 6041 to get a perfect square number, that is, 6084.