The supplied algorithm works just as well with integers or fixed-point.

An attempt with unsigned data type and the number 12714 gives:

0       12714   6357
1       6357    3179
2       3179    1591
3       1591    799
4       799     407
5       407     219
6       219     138
7       138     115
8       115     112
9       112     112
sqrt 12714 = 112 (112.756)

When integers are used, the answer will be truncated. It may be an idea to also try to take the answer+1 and square to decide which two integers will be closest.

An attempt at fixed point can also be done. Sqrt of 2.000000 results in:

0       2000000 1000000
1       1000000 500001
2       500001  250002
3       250002  125004
4       125004  62509
5       62509   31270
6       31270   15666
7       15666   7896
8       7896    4074
9       4074    2282
10      2282    1579
11      1579    1422
12      1422    1414
13      1414    1414
14      1414    1414
sqrt 2.000000 = 1.414 (1.41421)

The problem with fixed point is that the evaluation must be done with at least twice as many decimals as the expected end result, since a square doubles the number of digits.

In the end, it will be up to OP to figure out if the problem was to evaluate the square root of 24-bit integers, or if it was 24-bit fixed-point numbers or possibly tiny 24-bit floating-point numbers. I kind of assume that this is a school exercise, in which ase the optional conversion to fixed point and the rewrite into assembler will be required steps before the solution is turned in.