1. What is Square Root Calculation?

The square root of a number is a value that, when multiplied by itself, gives the original number. Calculating square roots with decimal precision is important for many mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses Newton's method (also known as the Heron's method):

Where:

• \( S \) — The number for which we're calculating the square root
• \( x_n \) — Current approximation
• \( x_{n+1} \) — Next, more accurate approximation

Explanation: The method iteratively improves the approximation until the desired precision is achieved.

3. Importance of Decimal Precision

Details: Different applications require different levels of precision. This calculator allows you to specify exactly how many decimal places you need for your calculations.

4. Using the Calculator

Tips: Enter a non-negative number and specify how many decimal places you need in the result. Higher precision values will take slightly longer to compute.

5. Frequently Asked Questions (FAQ)

Q1: Why use Newton's method instead of simple division?
A: Newton's method converges much faster to the precise value, especially for numbers that aren't perfect squares.

Q2: What's the maximum precision I can use?
A: The calculator allows up to 10 decimal places, which is sufficient for most practical applications.

Q3: How accurate is this method?
A: Extremely accurate - it will match built-in calculator functions when using sufficient precision.

Q4: Can I calculate square roots of negative numbers?
A: No, this calculator only handles real numbers. For complex numbers, you would need a different tool.

Q5: What's the advantage over PHP's built-in sqrt() function?
A: This lets you control the decimal precision directly and demonstrates the mathematical method behind the calculation.