**π‘ Problem Formulation:** How can we determine the nearest square root of a given non-negative number in Python with reasonable accuracy? The challenge is to write functions that can take a non-negative number as input, e.g., `24`

, and return an approximation of its square root, like `4.898`

, which rounds to the nearest whole number of `5`

.

## Method 1: Using the math.sqrt Function

The `math.sqrt`

method, found within Python’s built-in math module, precisely calculates the square root of a number. However, in the context of “guessing” the nearest square root, we can use this function as a benchmark for accuracy.

Here’s an example:

import math def guess_sqrt(n): return round(math.sqrt(n)) print(guess_sqrt(24))

Output: `5`

This code snippet imports the math module and defines a function called `guess_sqrt()`

that takes a number `n`

, calculates its square root using `math.sqrt()`

, and then rounds this value to the nearest whole number using Python’s built-in `round()`

function.

## Method 2: Using the Exponentiation Operator

Python’s exponentiation operator (`**`

) allows users to calculate the power of a number. In terms of finding a square root, we can raise a number to the power of `0.5`

(or `1/2`

) which is mathematically equivalent to calculating its square root. We then round the result to approximate the nearest square root.

Here’s an example:

def guess_sqrt(n): return round(n ** 0.5) print(guess_sqrt(24))

Output: `5`

The function `guess_sqrt()`

raises `n`

to the power of `0.5`

and rounds the result. This is a quick and efficient way to approximate the square root without importing any additional modules.

## Method 3: Using the Decimal Module

The Decimal module provides precise arithmetic calculations and can be used to find a square root to any desired level of accuracy by setting the context. After computing the square root as a decimal, we round to get the nearest whole number.

Here’s an example:

from decimal import Decimal, getcontext def guess_sqrt(n): getcontext().prec = 5 # Set precision to 5 places return round(Decimal(n).sqrt()) print(guess_sqrt(24))

Output: `5`

Here, we import the `Decimal`

class and `getcontext`

function from the `decimal`

module. We set the precision to 5 places, calculate the square root of `n`

using `Decimal(n).sqrt()`

, and then round it.

## Method 4: The Newtonβs Method (Iterative Approach)

Newtons Method, also known as the Heron’s method, is an iterative algorithm to approximate square roots. We make an initial guess and refine it using iterative calculations. It often yields high accuracy with relatively few iterations.

Here’s an example:

def guess_sqrt(n): x = n while True: root = 0.5 * (x + n/x) if abs(root - x) < 1e-5: return round(root) x = root print(guess_sqrt(24))

Output: `5`

This code snippet executes an iterative process based on Newton’s method. The loop continues until the difference between successive guesses is less than `1e-5`

. The approximation is then rounded to the nearest whole number.

## Bonus One-Liner Method 5: Using Python’s Built-in round() Function

A one-liner approach employs Python’s built-in `round()`

function, used in combination with the exponentiation operator for an immediate approximation of the square root; this approach is concise but effective for whole number approximations.

Here’s an example:

print(round(24 ** 0.5))

Output: `5`

This simple one-liner rounds the result of the exponentiation operator, which has raised the input number to the power of `0.5`

, thus calculating its square root and approximating it to the nearest whole number.

## Summary/Discussion

**Method 1:**math.sqrt. Precise. Requires import. Good benchmark.**Method 2:**Exponentiation Operator. Fast. No import needed. Less precise.**Method 3:**Decimal Module. Custom precision. Slightly more complex.**Method 4:**Newton’s Method. Very accurate. Iterative. More complex.**Method 5:**Built-in round(). Simplest. Least code. Rounded to whole numbers only.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.