#### Task:

Your job here is to implement a method, `approx_root` in Ruby/Python/Crystal and `approxRoot` in JavaScript/CoffeeScript, that takes one argument, `n`, and returns the approximate square root of that number, rounded to the nearest hundredth and computed in the following manner.

1.      Start with `n = 213` (as an example). 
2.      To approximate the square root of n, we will first find the greatest perfect square that is below or equal to `n`. (In this example, that would be 196, or 14 squared.) We will call the square root of this number (which means sqrt 196, or 14) `base`.
3.      Then, we will take the lowest perfect square that is greater than or equal to `n`. (In this example, that would be 225, or 15 squared.)
4.      Next, subtract 196 (greatest perfect square less than or equal to `n`) from `n`. (213 - 196 = **17**) We will call this value `diff_gn`.
5.      Find the difference between the lowest perfect square greater than or equal to `n` and the greatest perfect square less than or equal to `n`. (225 – 196 = **29**) We will call this value `diff_lg`.
6.      Your final answer is `base` + (`diff_gn` / `diff_lg`). In this example: 14 + (17 / 29) which is 14.59, rounded to the nearest hundredth.

Just to clarify, if the input is a perfect square itself, you should return the exact square of the input.

In case you are curious, the approximation (computed like above) for 213 rounded to four decimal places is 14.5862. The actual square root of 213 is 14.5945. 

Inputs will always be positive whole numbers. If you are having trouble understanding it, let me know with a comment, or take a look at the second group of the example cases.

#### Some examples:

```python
approx_root(400) #=> 20
approx_root(401) #=> 
  # smallest perfect square above 401 is 441 or 21 squared
  # greatest perfect square below 401 is 400 or 20 squared
  # difference between 441 and 400 is 41
  # difference between 401 and 400 is 1
  # answer is 20 + (1 / 41) which becomes 20.02, rounded to the nearest hundredth
  # final answer = 20.02.
approx_root(2) #=>
  # smallest perfect square above 2 is 4 or 2 squared
  # greatest perfect square below 2 is 1 or 1 squared
  # difference between 4 and 1 is 3
  # difference between 2 and 1 is 1
  # answer is 1 + (1 / 3), which becomes 1.33, rounded to the nearest hundredth
  # final answer = 1.33.

# math.sqrt() isn't disabled.
```

Also check out my other creations — [Square Roots: Simplifying/Desimplifying](https://www.codewars.com/kata/square-roots-simplify-slash-desimplify/), [Square and Cubic Factors](https://www.codewars.com/kata/square-and-cubic-factors), [Keep the Order](https://www.codewars.com/kata/keep-the-order), [Naming Files](https://www.codewars.com/kata/naming-files), [Elections: Weighted Average](https://www.codewars.com/kata/elections-weighted-average), [Identify Case](https://www.codewars.com/kata/identify-case), [Split Without Loss](https://www.codewars.com/kata/split-without-loss), [Adding Fractions](https://www.codewars.com/kata/adding-fractions),
[Random Integers](https://www.codewars.com/kata/random-integers), [Implement String#transpose](https://www.codewars.com/kata/implement-string-number-transpose), [Implement Array#transpose!](https://www.codewars.com/kata/implement-array-number-transpose), [Arrays and Procs #1](https://www.codewars.com/kata/arrays-and-procs-number-1), and [Arrays and Procs #2](https://www.codewars.com/kata/arrays-and-procs-number-2).

If you notice any issues or have any suggestions/comments whatsoever, please don't hesitate to mark an issue or just comment. Thanks!

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def approx_root(n):\n    base = int(n ** 0.5)\n    diff_gn = n - base ** 2\n    diff_lg = base * 2 + 1\n    return round(base + diff_gn / diff_lg, 2)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'approx_root'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5422