Newton’s method of calculating a square root.

5² = 25, so √25 = 5, or expressed another way, 5 * 5 = 25, so the square root of 25 is 5. Newton’s method is one way to calculate the square root of a number.

Square root

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Make

Write a program that outputs the square root of a number using Newton’s method.

Success Criteria

Remember to add a comment before a subprogram, selection or iteration statement to explain its purpose.

Complete the subprogram called sqroot that:

  1. Takes the parameter x which is the number to square root.
  2. root = x at the start of the algorithm.
  3. root is repeatedly recalculated as 0.5 * (root + (x / root)) until the value of root does not change.

For example, the square root of 64 can be calculated in the sequence of steps:

64

32.5

17.234615384615385

10.474036101145005

8.292191785986859

8.005147977880979

8.000001655289593

8.00000000000017

8.0

8.0 – This value equals the previous value of root, so the algorithm is complete.

Complete the main program so that:

  1. The user can input a positive decimal number to square root.
  2. The square root is output.

Typical inputs and outputs from the program would be:

Enter a number: 25
The square root of 25.0 is 5.0

Enter a number: 64
The square root of 64.0 is 8.0