Square root

Square root

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.


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

Use this boilerplate code as a starting point:

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:










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

Knowledge Organiser

Use these resources as a reference to help you meet the success criteria.

Programming guide:


Run the unit tests below to check that your program has met the success criteria.

Enter a number: 18.49

The square root of 18.49 is 4.3

Enter a number: 36

The square root of 36.0 is 6.0

Enter a number: 49

The square root of 49.0 is 7.0

Enter a number: 200

The square root of 200.0 is 14.142135623730951

Check that you have:

  • Used comments within the code to describe the purpose of subprograms, conditions and iterations.
  • Used meaningful identifier names. That means the names of subprograms and variables indicate what they are for.
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