Multiplying and Dividing Radicals Calculator

Radical Operations:

\[ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \] \[ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \]

Result:

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1. What Are Radical Operations?

Radical operations involve mathematical operations with square roots (√). The two fundamental operations are multiplication and division of square roots, which follow specific algebraic rules.

2. How Radical Multiplication Works

The product of two square roots equals the square root of the product:

\[ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \]

Example: √4 × √9 = √(4×9) = √36 = 6

3. How Radical Division Works

The quotient of two square roots equals the square root of the quotient:

\[ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \]

Example: √25 ÷ √5 = √(25/5) = √5 ≈ 2.236

4. Using This Calculator

Steps:

Select operation (multiplication or division)
Enter values for a and b (must be non-negative)
Click "Calculate" to see the result

5. Frequently Asked Questions (FAQ)

Q1: Can I multiply radicals with different indices?
A: This calculator only handles square roots (index 2). Different indices require more complex calculations.

Q2: What if my radicand is negative?
A: The calculator only accepts non-negative values since square roots of negative numbers involve complex numbers.

Q3: How do I simplify radicals?
A: The calculator automatically simplifies the result. For manual simplification, factor out perfect squares.

Q4: Can I add radicals using this calculator?
A: No, this calculator only handles multiplication and division. Addition follows different rules (√a + √b ≠ √(a+b)).

Q5: Why does division require b ≠ 0?
A: Division by zero is undefined in mathematics, so b must be positive for division operations.