question_answer 2)

                The following numbers an obviously not perfect squares. Give reason. (i) 1057                                 (ii) 23453                              (iii) 7928                              (iv) 222222 (v) 64000                              (vi) 89722                             (vii) 222000        (viii) 505050.

Answer:

                (i) 1057 The number 1057 is not a perfect square because it ends with 7 whereas the square numbers end with 0, 1, 4, 5, 6 or 9. (ii) 23453 The number 23453 is not a perfect square because it ends with 3 whereas the square numbers end with 0, 1, 4, 5, 6 or 9. (iii) 7928 The number 7928 is not a perfect square because it ends with 8 whereas the square numbers end with 0, 1, 4, 5, 6 or 9. (iv) 222222 The number 222222 is not a perfect square because it ends with 2 whereas the square numbers end with 0, 1, 4, 5, 6 or 9. (v) 64000 The number 64000 is not a square number because the number of zeros at the end of a square number ending with zeroes is always even. (vi) 89722 The number 89722 is not a square number because it ends in 2 whereas the square numbers end with 0, 1, 4, 5, 6 or 9. (vii) 222000 The number 222000 is not a square number because it has 3 (an odd number of) zeroes at the end whereas the number of zeroes at the end of a square number ending with zeros is always even. (viii) 505050 The number 505050 is not a square number because it has 1 (an odd number of) zeroes at the end whereas the number of zeroes at the end of a square number ending with zeros is always even.