Multiplying Radicals Calculator
Multiply radical expressions and simplify the result
2 = square root (√), 3 = cube root (³√), 4 = fourth root (⁴√), etc.
How to Use This Calculator
Enter First Value
Input the value under the radical in the first expression. This is the number inside the radical sign in the first factor.
Enter Second Value
Input the value under the radical in the second expression. This is the number inside the radical sign in the second factor.
Specify Index
Enter the index (root type): 2 for square root (√), 3 for cube root (³√), 4 for fourth root, etc. Default is 2 (square root).
Get Result
Click "Calculate" to see the simplified radical form and decimal value of the multiplication.
Formula
n√a × n√b = n√(a × b)
Where:
- n = index (root type: 2 for square root, 3 for cube root, etc.)
- a = value under the radical in first expression
- b = value under the radical in second expression
Example 1: √2 × √8
√2 × √8 = √(2 × 8) = √16 = 4
Verification: 1.414 × 2.828 ≈ 4 ✓
Example 2: ³√4 × ³√2
³√4 × ³√2 = ³√(4 × 2) = ³√8 = 2
Verification: 1.587 × 1.260 ≈ 2 ✓
Example 3: √3 × √12
√3 × √12 = √(3 × 12) = √36 = 6
This simplifies the radicals before multiplying
About Multiplying Radicals Calculator
The Multiplying Radicals Calculator helps you multiply radical expressions (square roots, cube roots, etc.) that have the same index. When multiplying radicals with the same index, you can multiply the values under the radicals and keep the same index. This calculator simplifies the process and provides both simplified radical form and decimal approximations.
When to Use This Calculator
- Algebra: Simplify expressions like √6 × √24 when solving equations
- Geometry: Multiply radical expressions in distance or area calculations
- Calculus: Simplify radical expressions before differentiating or integrating
- Mathematical Simplification: Reduce complex radical expressions to simpler forms
- Test Preparation: Practice radical multiplication for standardized tests
Why Use Our Calculator?
- ✅ Instant Results: Get accurate radical multiplication immediately
- ✅ Simplified Form: Shows the result in simplest radical form
- ✅ Decimal Approximation: Provides decimal value for practical use
- ✅ Multiple Root Types: Supports square roots, cube roots, and any nth root
- ✅ Educational: Learn radical multiplication rules through examples
- ✅ 100% Free: No registration or payment required
Common Applications
Algebra: When solving equations like √(2x) × √(8) = 6, you can simplify: √(16x) = 6, so 16x = 36, which means x = 2.25.
Geometry: When calculating areas or volumes involving radicals, multiplying radicals simplifies the calculations. For example, area = √2 × √8 = √16 = 4.
Physics: In calculations involving wave functions or oscillations, you may need to multiply radical expressions to simplify formulas.
Tips for Best Results
- The radicals must have the same index to use this rule
- Always simplify after multiplying when possible (e.g., √2 × √8 = √16 = 4)
- For even roots, ensure the values under the radicals are non-negative
- After multiplying, check if the result can be simplified further
- This rule makes calculations much easier than multiplying each radical separately
Frequently Asked Questions
How do I multiply radicals with the same index?
When radicals have the same index, multiply the values under the radicals: n√a × n√b = n√(a × b). For example, √2 × √8 = √(2 × 8) = √16 = 4.
Can I multiply radicals with different indexes?
You need to convert them to the same index first. For example, to multiply √8 by ³√2, convert both to ⁶√(8³) × ⁶√(2²) = ⁶√512 × ⁶√4 = ⁶√2048.
What if I get a perfect square under the radical?
Perfect! You should simplify it. For example, √2 × √18 = √36 = 6. Always simplify radicals when possible.
Can the result be simplified after multiplying?
Yes! Always check if the result can be simplified. For example, √3 × √12 = √36 = 6, which is much simpler than leaving it as √36.
What about negative numbers under even roots?
Even roots (square root, fourth root, etc.) of negative numbers are not real numbers. Make sure both values are non-negative when using even roots.