Multiply and Simplify Square Roots Calculator
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Reviewed by Calculator Editorial Team
This calculator helps you multiply and simplify square roots by following the product rule of square roots. Enter your square roots, and the calculator will show you the simplified product.
How to Use This Calculator
To use the multiply and simplify square roots calculator:
- Enter the first square root in the first input field (e.g., √8)
- Enter the second square root in the second input field (e.g., √18)
- Click the "Calculate" button
- View the simplified product result
The calculator will automatically simplify the product of the two square roots using the product rule of square roots.
Formula Explained
The product rule of square roots states that:
When multiplying two square roots, you can combine them into a single square root of the product of the radicands. The calculator then simplifies this product by factoring out perfect squares.
For example, multiplying √8 and √18:
Worked Examples
Example 1: Simple Multiplication
Multiply √9 and √16:
Example 2: Simplification Needed
Multiply √12 and √27:
Notice how the calculator simplifies the product by factoring out perfect squares.
Frequently Asked Questions
What is the product rule of square roots?
The product rule of square roots states that the product of two square roots is equal to the square root of the product of the radicands. Mathematically, √a × √b = √(a × b).
How do I simplify the product of square roots?
To simplify the product of square roots, multiply the radicands together and then factor out any perfect squares. For example, √8 × √18 = √(8 × 18) = √144 = 12.
Can I multiply more than two square roots?
Yes, you can multiply any number of square roots by combining them into a single square root of the product of all radicands. For example, √a × √b × √c = √(a × b × c).
What if the radicands are not perfect squares?
If the product of the radicands is not a perfect square, the simplified form will remain as a square root. For example, √2 × √3 = √6, which cannot be simplified further.