Exercise 05-25:
Write a program that calculates the square root of a number, using Newton’s method to get an approximate result. Since n is the number to obtain the square root, consider the base b = 2. Calculate p using the formula p = (b + (n/b)) / 2. Now, calculate the square of p. At each step, do b = p and recalculate p using the formula presented. Stop when the absolute difference between n and the square of p is less than 0.0001.
Answer:
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# Python From Scratch
# Author: Nilo Ney Coutinho Menezes
# Editora Novatec (c) 2010-2025 - LogiKraft 2025
# Site: https://pythonfromscratch.com
# ISBN: 978-85-7522-949-1 (Paperback), 978-85-7522-950-7 (hardcover), 978-85-7522-951-4 (ebook)
#
# File: chapter 05/exercise-05-25.py.py
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# The abs function is used to calculate the absolute value of a number,
# that is, its value without sign.
# Examples: abs(1) returns 1 and abs(-1) returns 1
n = float(input("Enter a number to find its square root: "))
b = 2
while abs(n - (b * b)) > 0.00001:
p = (b + (n / b)) / 2
b = p
print(f"The square root of {n} is approximately {p:8.4f}")