Question

please please solve this question and let me also I don't know please step by step please solve this question ​

Answer 1

$\sf{\pink{\underline{\underline{Given:}}}}$

The following numbers are obviously not perfect squares. Give reasons:

1. 1057
2. 23453
3. 7928
4. 222222
5. 64000
6. 89722
7. 222000
8. 505050

$\sf{\blue{\underline{\underline{To\:find:}}}}$

Prove that the numbers are not perfect squares.

$\sf{\orange{\underline{\underline{Answer:}}}}$

Properties to know if a number is a perfect square:

1. A number ending with 2 is never a perfect square
2. A number ending with 3 is never a perfect square
3. A number ending with 7 is never a perfect square
4. A number ending with 8 is never a perfect square
5. A number ending in an odd number of zeroes is never a perfect square.

$\sf{\underline{Answer}}$

1. From property 3, as it is ending with 7, it is not a perfect square.
2. From property 2, as it is ending with 3, it is not a perfect square.
3. From property 4, as it is ending with 8, it is not a perfect square.
4. From property 1, as it is ending with 2, it is not a perfect square.
5. From property 5, as it is ending with odd number of zeroes (3 zeroes), it is not a perfect square.
6. From property 1, as it is ending with 2, it is not a perfect square.
7. From property 5, as it is ending with odd number of zeroes (3 zeroes), it is not a perfect square.
8. From property 5, as it is ending with odd number of zeroes (1 zeroes), it is not a perfect square.