1. What is a System of Radicals?

A system of radicals involves equations with roots (typically square roots) of variables. The equation √x + √y = z is a simple example where we check the relationship between three variables through their square roots.

2. How Does the Calculator Work?

The calculator evaluates the equation:

Where:

• \( x \) — First radicand (must be ≥ 0)
• \( y \) — Second radicand (must be ≥ 0)
• \( z \) — Sum of square roots (must be ≥ 0)

Explanation: The calculator computes both sides of the equation and checks if they are equal within a small tolerance to account for floating-point precision.

3. Importance of Radical Equations

Details: Radical equations appear in various mathematical and scientific contexts, including geometry (diagonal distances), physics (kinetic energy), and engineering (signal processing).

4. Using the Calculator

Tips: Enter non-negative values for x, y, and z. The calculator will verify if the equation holds true or show the actual computed value.

5. Frequently Asked Questions (FAQ)

Q1: What if I get negative numbers?
A: The square root of negative numbers is not real, so all inputs must be ≥ 0.

Q2: Why might the equation not hold exactly?
A: Due to floating-point precision in computers, very small differences might occur even when the equation should theoretically hold.

Q3: Can this solve for variables?
A: This calculator verifies given values. To solve for variables, you would need algebraic manipulation.

Q4: What's the maximum input size?
A: There's no strict limit, but extremely large numbers might cause precision issues.

Q5: Can this handle complex numbers?
A: No, this calculator only works with real numbers.