Square Root Calculator

Goals:

• Recognize iterative and recursive methods in Java
• Write recursive methods in Java

Instructions:

The square root of a number can be found recursively without too much trouble. The idea is to make an initial guess (called previousGuess in the pseudocode). You then make a next guess (called nextGuess) based on the previous guess and the original number. You repeat this process until the difference between guesses is a very small positive number.

Write a Java program which finds the square root of a positive number recursively using the following outline/pseudo code:

• Create an array of numbers. The numbers in the array will be: 9, 17, 25, 37, 49, 55, 999
• Using a for loop find the square root of each number in the array using this procedure
  • Calculate a guess of the root by generating a random number between 1 and the first number in the array. Call this number previousGuess
  • Print the number and the first Guess
  • Call a method called FindtheRoot...this is the recursive method
    • send the method previousGuess and the number whose root you are finding
    • this method will calculate and return the square root of the given number.
    • DO NOT use a built in math function
    • You must use recursion for full credit (although there are other ways to process this)
  • Print:
    • the number
    • the returned root formatted to display 4 places to the right of the decimal (ten thousandths)
    • label the output with appropriate text
  • Process the next number in the array
• FindTheRoot
  • We need 2 "guesses" at the square root so we can compare them.
    • Calculate the next guess using the formula
    • next guess will be equal to: (your previous guess + target number/your previous guess)/2
  • If the difference of the two guesses(previous and next) is less than 0.00001 apart (but must be positive)
    • return the next guess as the square root
  • If the difference is not less than 0.00001 apart then
  • Print:
    • the next guess formatted to display 4 places to the right of the decimal (ten thousandths) - label the output with appropriate text
    • call FindTheRoot sending it the nextguess and the target number...this is the recursive call
    • return the value sent back from the call to the method
• Sample output. Our roots will all be the same but our numbers to get there will differ

Sample output: see image.