Multiply and Simplify by Factoring Square Roots Calculator

This calculator helps you multiply square roots and simplify the result by factoring. It follows the mathematical rules for handling square roots and provides step-by-step guidance.

How to Use This Calculator

To use the calculator:

Enter the first square root in the first input field (e.g., √12)
Enter the second square root in the second input field (e.g., √18)
Click the "Calculate" button
Review the simplified result and the step-by-step solution

The calculator will multiply the square roots and simplify the result by factoring out perfect squares.

How It Works

When multiplying two square roots, you can combine them into a single square root:

√a × √b = √(a × b)

After multiplying, you can simplify the expression by factoring out perfect squares from the radicand (the number under the square root).

For example, if you have √(12 × 18), you can factor the numbers:

12 = 4 × 3
18 = 9 × 2
√(12 × 18) = √(4 × 3 × 9 × 2) = √(4 × 9 × 6) = √(36 × 6) = 6√6

The calculator performs these steps automatically for any two square roots you input.

Worked Examples

Example 1: √8 × √2

Step 1: Multiply the radicands: √(8 × 2) = √16

Step 2: Simplify √16 to 4

Final result: 4

Example 2: √18 × √8

Step 1: Multiply the radicands: √(18 × 8) = √144

Step 2: Simplify √144 to 12

Final result: 12

Example 3: √50 × √2

Step 1: Multiply the radicands: √(50 × 2) = √100

Step 2: Simplify √100 to 10

Final result: 10

Frequently Asked Questions

Can I multiply more than two square roots with this calculator?

This calculator is designed for multiplying two square roots. For more than two, you would need to multiply them sequentially.

What if the result is not a perfect square?

The calculator will simplify the expression as much as possible by factoring out perfect squares, but the final result may still contain a square root.

Can I use negative numbers with this calculator?

Square roots of negative numbers are not real numbers. The calculator only accepts positive numbers.