1. What is Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9.

2. How Does the Calculator Work?

The calculator uses the mathematical square root function:

Where:

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

Explanation: The calculator uses PHP's built-in sqrt() function to compute the square root with high precision.

3. Importance of Square Root Calculation

Details: Square roots are fundamental in mathematics and have applications in geometry, physics, engineering, statistics, and many scientific calculations. They're essential for solving quadratic equations and appear in formulas for areas, distances, and standard deviations.

4. Using the Calculator

Tips: Enter any non-negative number (including decimals) to calculate its square root. The result will be displayed with up to 4 decimal places for 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), which this calculator doesn't handle.

Q2: How precise are the results?
A: Results are accurate to at least 4 decimal places, which is sufficient for most practical applications.

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

Q4: How is this different from other root calculations?
A: Square root specifically finds the second root (n=2). Other roots like cube root (n=3) would require different calculations.

Q5: Why do some numbers have irrational square roots?
A: Perfect squares have integer roots, but most numbers have irrational roots (non-repeating, non-terminating decimals) because they can't be expressed as exact fractions.