The number is 43

We have ##50^2=2500##, and ##40^2=1600##.

Midpoint is ##45^2 > 1849##.

So it must be between 40 and 45.

The terminal digit squared## = 9##. So if the root is an integer, that number is 43.

Testing ##43^2 = 1849## confirms that this is the required root.

The number is 43

We have ##50^2=2500##, and ##40^2=1600##.

Midpoint is ##45^2 > 1849##.

So it must be between 40 and 45.

The terminal digit squared## = 9##. So if the root is an integer, that number is 43.

Testing ##43^2 = 1849## confirms that this is the required root.