This Python program finds all perfect squares within a given range (inclusive) and displays them as a list. A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 4, 9, 16, and 25 are perfect squares because they can be expressed as 2×2, 3×3, 4×4, and 5×5, respectively.

## Program Statement

Given a range specified by the start and end values, we need to find all perfect squares within that range (including both the start and end values) and display them as a list.

## Python Program to Find All Perfect Squares in the Given Range

import math def find_perfect_squares(start, end): squares = [] # Find the square root of the start and end values # Round up the square root of the start value # Round down the square root of the end value # This will give us the range of numbers to check for perfect squares start_root = math.ceil(math.sqrt(start)) end_root = math.floor(math.sqrt(end)) # Iterate through the range and check if each number is a perfect square for num in range(start_root, end_root + 1): if num * num >= start and num * num <= end: squares.append(num * num) return squares # Example usage start_range = 1 end_range = 100 result = find_perfect_squares(start_range, end_range) print("Perfect squares between", start_range, "and", end_range, "are:", result)

## How it works

- Import the
`math`

module, which provides mathematical functions including square root calculation. - Define a function called
`find_perfect_squares`

that takes two parameters:`start`

and`end`

. - Inside the function, initialize an empty list called
`squares`

to store the perfect squares. - Calculate the square root of the
`start`

value using`math.sqrt()`

and round it up using`math.ceil()`

. Assign the result to`start_root`

. - Calculate the square root of the
`end`

value using`math.sqrt()`

and round it down using`math.floor()`

. Assign the result to`end_root`

. - Iterate through the range from
`start_root`

to`end_root + 1`

. - For each number in the range, check if its square falls within the given range (
`start`

and`end`

). - If the square of the number falls within the range, append it to the
`squares`

list. - After iterating through all the numbers, return the
`squares`

list. - Outside the function, prompt the user to enter the
`start_range`

and`end_range`

values. - Call the
`find_perfect_squares`

function with the entered`start_range`

and`end_range`

values, and assign the result to a variable`result`

. - Print the start and end range values.
- Print the list of perfect squares found within the range.

The program calculates the square root of the start and end values to determine the range of numbers to check for perfect squares. It then iterates through this range, checks if each number squared falls within the given range, and appends the perfect squares to a list. Finally, it displays the list of perfect squares found within the given range.

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