Question

Find the least number which must be added to the following numbers to make them a perfect square:
(i) 5607
(ii) 4931
(iii) 4515600
(iv) 37460
(v) 506900

Answer 1

(i) Using the long division method:

We can see that 5607 is 18 more than 75². Hence, we have to add 18 to 5607 to get a perfect square.

(ii) Using the long division method:

We can see that 4931 is 110 more than 71². Hence, we have to add 110 to 4931 to get a perfect square.

(iii) Using the long division method:

We can see that 4515600 is 25 more than 2125². Hence, we have to add 25 to 4515600 to get a perfect square.

(iv) Using the long division method:

We can see that 37460 is 176 more than 194². Hence, we have to add 176 to 37460 to get a perfect square.

(v) Using the long division method:

We can see that 506900 is 44 more than 712². Hence, we have to add 44 to 506900 to get a perfect square.