Question

The following numbers are not perfect squares. Give reasons to support your answer.
A.$1057$
B.$23453$
C.$7928$
D.$222222$
E.$64000$
F.$89722$
G.$222000$
H.$505050$

Answer 1

Hint: Here make use of the concept that for a number to be a perfect square it should end with either $1,4,5,6,9,00$ (even number of 0’s).


Complete step-by-step answer:
$1057$
The number $1057$ends with 7 and does not end with either $1,4,5,6,9,00$ or even a number of 0’s.
Therefore, it cannot be a perfect square.

$23453$
The number $23453$ ends with 3 and does not end with either $1,4,5,6,9,00$ or even number of 0’s.
Therefore, it cannot be a perfect square.

$7928$
The number $7928$ ends with 8 and does not end with either $1,4,5,6,9,00$ or even a number of 0’s.
Therefore, it cannot be a perfect square.

$222222$
The number $222222$ ends with 2 and does not with either $1,4,5,6,9,00$ or even number of 0’s at the end.
Therefore, it cannot be a perfect square.

$64000$
The number $64000$ ends with three 0’s and does not with either $1,4,5,6,9,00$ or even number of 0’s at the end.
Therefore, it is not a perfect square.

The number $89722$ ends with 2 and does not with $1,4,5,6,9,00$ or even number of 0’s at the end.
Therefore, it is not a perfect square.

$222000$
The number $222000$ ends with 3 zero’s and not with $1,4,5,6,9,00$ or even number of 0’s.
Therefore, it is not a perfect square.

$505050$
The number $505050$ ends with only 1 zero and not with $1,4,5,6,9,00$ or even number of 0’s.
Therefore, it is not a perfect square.


Note: The number to be a perfect square should satisfy the first condition that it should end with either $1,4,5,6,9,00$ or even a number of zeroes.
Also, the digital roots of the number should be $1,4,7$or $9$ . Digital roots can be obtained by adding all the digits of a number and then again adding all its digits until it becomes a one digit number.