Q.5 Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

(i) 525

(ii) 1750

(iii) 252

(iv) 1825

(v) 6412

Answers (1)

(i) 525:-    It is clearly visible that if we add 4 to the given number, the remainder will become zero.

                  So obtained number is 529 and its square root is 23.(ii) 1750:-    It is clearly visible that if we add 14 to the given number, the remainder will become zero.

                  So the obtained number is 1764 and its square root is 42.

(iii) 252:-  It is clearly visible that if we add 4 to the given number, the remainder will become zero.

                  So the obtained number is 256 and its square root is 16.

(iv) 1825:-  It is clearly visible that if we add 24 to the given number, the remainder will become zero.

                  So the obtained number is 1849 and its square root is 43.

(v)  6412:-   It is clearly visible that if we add 149 to the given number, the remainder will become zero.

                     So the obtained number is 6561 and its square root is 81.

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