Newton's method of calculating a square root.

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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.

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.

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

# Square root program

# -------------------------
# Subprograms
# -------------------------
# Function to calculate the square root of a number using Newton's method
---
def sqroot(x):
---
    root = x
    last_root = 0
---
    while root != last_root:
---
        last_root = root
---
        root = 0.5 * (root + (x / root))
---
    return root
---


# -------------------------
# Main program
# -------------------------
---
num = float(input("Enter a number: "))
---
print("The square root of", num, "is", sqroot(num))