1. What is a Radical Expression?

A radical expression is an expression that contains a square root, cube root, or other root symbol. The square root of a number x is a number y such that y² = x.

2. How Does the Calculator Work?

The calculator uses the mathematical principle:

Where:

• \( x \) — The number under the radical (radicand)
• \( y \) — The square root result

Explanation: For any non-negative real number x, its square root is the non-negative number y that when multiplied by itself equals x.

3. Importance of Square Roots

Details: Square roots are fundamental in mathematics, used in algebra, geometry, physics, engineering, and many real-world applications like calculating distances and areas.

4. Using the Calculator

Tips: Enter any positive number to calculate its principal (non-negative) square root. The calculator will return the exact value or a decimal approximation.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a negative number?
A: The calculator will only process non-negative inputs. Square roots of negative numbers are complex numbers (involving i).

Q2: How precise are the results?
A: Results are rounded to 4 decimal places for readability while maintaining reasonable precision.

Q3: What about perfect squares?
A: For perfect squares (like 4, 9, 16), the calculator will return exact integer results.

Q4: Can this calculate cube roots or higher?
A: This version only calculates square roots. Future versions may include other root calculations.

Q5: How is this different from estimating square roots?
A: This calculator computes precise values using PHP's built-in sqrt() function, not estimation methods.