1. What Are Radical Operations?

Radical operations involve mathematical operations with square roots (√). The main operations are addition, subtraction, and multiplication of radicals. These operations follow specific algebraic rules that differ from regular numbers.

2. How Does the Calculator Work?

The calculator performs three fundamental radical operations:

Where:

• \( a \) — Radicand (value under the radical) of the first term
• \( b \) — Radicand of the second term
• All values must be non-negative (≥0)

Note: For addition and subtraction, radicals can only be combined directly if they have the same radicand. Multiplication follows the product rule for radicals.

3. Importance of Radical Calculations

Details: Understanding radical operations is essential in algebra, geometry, physics, and engineering. They appear in quadratic equations, distance formulas, and many real-world applications involving square relationships.

4. Using the Calculator

Tips: Enter non-negative values for a and b, select the desired operation. The calculator will compute the exact form (with radicals) and the decimal approximation.

5. Frequently Asked Questions (FAQ)

Q1: Can I add √2 and √3 directly?
A: No, √2 + √3 cannot be simplified further as they have different radicands. The result remains √2 + √3.

Q2: What's the rule for multiplying radicals?
A: The product of two square roots equals the square root of the product: √a × √b = √(a×b).

Q3: Can this calculator handle variables?
A: No, this calculator only works with numerical values. For variables, you would follow the same algebraic rules.

Q4: What about division of radicals?
A: Division follows a similar rule to multiplication: √a/√b = √(a/b), provided b ≠ 0.

Q5: How are negative numbers handled?
A: The calculator only accepts non-negative inputs since square roots of negative numbers involve complex numbers.