Question

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

Answer 1

We know that, numbers having $2,3,7or8$ at units place are not perfect squares.

That is because:

$1^2=1$

$2^2=4$

$3^2=9$

$4^2=16$

$5^2=25$

$6^2=36$

$7^2=49$

$8^2=64$

$9^2=81$

Also,

${10}^2=100$

${100}^2=10000$

Hence, any perfect square will end with $1,4,5,6,9$ or even number of zeros.

All the given numbers end with either $2,3,7,8$ or with odd number of zeros.

Hence, the given numbers are not perfect squares.