1. What is a Square Root Function?

Definition: The square root of a number is a value that, when multiplied by itself, gives the original number.

Purpose: Square roots are used in mathematics, physics, engineering, and many scientific calculations.

2. How Does the Square Root Work?

The square root is calculated using the formula:

Where:

• \( a \) — The number you want to find the square root of (must be ≥ 0)
• \( x \) — The square root result

Explanation: For any positive number, there are actually two square roots - a positive and negative value (e.g., √9 = 3 and -3). This calculator returns the principal (positive) square root.

3. Importance of Square Root Calculation

Details: Square roots are fundamental in geometry (Pythagorean theorem), statistics (standard deviation), physics (root mean square calculations), and many other fields.

4. Using the Calculator

Tips: Simply enter any positive number (including decimals) and click Calculate. The result will show the square root with 6 decimal places precision.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate square roots of negative numbers?
A: Not with real numbers. The square root of a negative number involves imaginary numbers (i = √-1).

Q2: How precise is the calculation?
A: The calculator shows results with 6 decimal places, but internal calculations use PHP's full precision.

Q3: What's the square root of zero?
A: √0 = 0, since 0 × 0 = 0.

Q4: How are square roots calculated computationally?
A: Computers typically use iterative methods like the Newton-Raphson method to approximate square roots.

Q5: What's the relationship between squares and square roots?
A: They are inverse operations - squaring a number and taking the square root cancel each other out.