Without finding a square root, let us find the possible digits in the units place and the number of digits in the square root number.

$784$

Without finding a square root, let us find the possible digits in the units place and the number of digits in the square root number.

$3676$

Without finding a square root, let us find the possible digits in the units place and the number of digits in the square root number.

$160000$

Without finding a square root, let us find the possible digits in the units place and the number of digits in the square root number.

$1225$

Without finding a square root, let us find the possible digits in the units place and the number of digits in the square root number.

$2401$

Without finding a square root, let us find the possible digits in the units place and the number of digits in the square root number.

$10201$

Let us find two square numbers nearest to $5000$.