Skip to main content

Finding square root of a number by Babylonian method

The Babylonian method for finding square roots involves dividing and averaging, over and over, to obtain a more accurate solution with each repeat of the process.
Inorder to find the square root of a number you need to follow the following steps.
  1. Make an initial guess for the square root 
  2. Divide the original number by this guess
  3. Find out the mean of the 2 numbers
  4. check if the difference between guess and quotient is less than the error if not then repeat the process again.
  5. use this mean value as your next guess
Let us take an example of finding out the square root of 7 to 3 decimal places

let n = 7 and error = 0.001
let us take an initial guess = 3
FIRST ITERATION
Step 1: Guess = 3 
Step 2: Divide 7 by 3 = 2.3333333
Step 3: Find average of 3 and 2.333333 = 2.666666 (because (2+2.333333)/2 = 2.666666)
Step 4: difference (3 - 2.3333333) > error hence repeat the process again
Step 5: Next guess is 2.666666

SECOND ITERATION
Step 1: Guess 2.666666
Step 2: Divide 7 by 2.666666 = 2.624999 
Step 3: Find average of 2.666666 and 2.624999 = 2.645832
Step 4: difference (2.666666 - 2.624999) > error hence repeat the process again
Step 5: Next guess is 2.645832

THIRD ITERATION
Step 1: Guess 2.645832
Step 2: Divide 7 by 2.645832 = 2.645670
Step 3: Find average of 2.645832 and 2.645670 = 2.645751
Step 4: difference (2.645832 - 2.645670) < error hence stop and print the answer
Step 4: FINAL guess is 2.645751

Now CHECK your final guess with a calculator: sqrt 7 = 2.645751

C Program

C++ Program

Sample input and output to check the program
Labels:

Comments

Post a Comment

Popular posts from this blog

Home Page

List of All Programs The Following is the List of all the programs on my Blog Math Programs Square Root of a number using Babylonian Method Finding The Next Smallest Palindrome Finding the Armstrong Numbers Factorial of a number GCD using Euclid's Algorithm Check if a number is Fibonacci Number or not LCM of 2 numbers Trailing Zeros in factorial of a number Sorting Algorithms Bubble Sort Algorithm Selection Sort Algorithm Insertion Sort Algorithm Shell Sort Algorithm Counting Sort Algorithm Linked List Programs Simple Singly Linked List Linked List in C++ Linked List in Python Linked List in Java Doubly Linked List Finding Kth element from the end of Linked List Delete a node from Linked List Delete Kth element from the end of Linked List Rotate Linked List in an Anti-clockwise direction Reversing first K nodes of a Linked List Binary Search Tree Left View of Binary Tree Righ...
4 comments
Read more

Hashing with Quadratic Probing

Hashing is a technique used for storing , searching and removing elements in almost constant time. Hashing is done with help of a hash function that generates index for a given input, then this index can be used to search the elements, store an element, or remove that element from that index. A hash function is a function that is used to map the data elements to their position in the data structure used. For example if we use an array to store the integer elements then the hash function will generate position for each element so that searching, storing and removing operation on the array can be done in constant time that is independent of the number of elements in the array. For better look at the example below. now we face a problem if for 2 numbers same position is generated example consider elements 1 and 14 1 % 13 = 1 14 % 13 = 1 so when we get 1 we store it at the first position, but when we get 14 we see that the position 1 is already taken, this is a case of colli...
Post a Comment
Read more

Hashing with Linear Probing

Hashing is a technique used for storing , searching and removing elements in almost constant time. Hashing is done with help of a hash function that generates index for a given input, then this index can be used to search the elements, store an element, or remove that element from that index. A hash function is a function that is used to map the data elements to their position in the data structure used. For example if we use an array to store the integer elements then the hash function will generate position for each element so that searching, storing and removing operation on the array can be done in constant time that is independent of the number of elements in the array. For better look at the example below. now we face a problem if for 2 numbers same position is generated example consider elements 1 and 14 1 % 13 = 1 14 % 13 = 1 so when we get 1 we store it at the first position, but when we get 14 we see that the position 1 is already taken, this is a case of colli...
Post a Comment
Read more