Roots - Learn What A Product Of Square Roots Is And How To Use The Square Roots Calculator

How Do We Compute The Product Of Square Roots?

Before we move forward and learn about Product Of Square Roots, be sure you understand the basics. Recommended reading: Square Roots.

The root of a product is the product of the roots.
A real example of taking a square root of a product: √(4 × 9) = √4 × √9 = √4√9 = 2 × 3 = 6.
Another real example of taking a square root of a product: √192 = √(2 × 2 × 2 × 2 × 2 × 2 × × 3) = 2 × 2 × 2 × √3 = 8√3. This is a fairly complex example. However, it can easily be solved by computing the Prime Factorization of 192.
There is no way to combine the square root sum of two numbers (like we can with products). You can simplify: √(3 + 2) = √5.
There is no way to combine the square root difference of two numbers (like we can with products). You can simplify: √(3 - 2) = √1 = 1.

Syntax Example
Combined As Products?	Math Expression	Answer
Yes	√192	8√3
Yes	2√(5 × 3)	2√15
Yes	√(9 × 16)	√9 × √16 = √9√16 = 3 × 4 = 12
No	√(5 + 4)	√9 = 3
No	√(5 - 4)	√1 = 1

Please Read! To use this calculator is easy. You can use any input format shown in the table above. You indicate the radical sign with the letter "r". Example 10r(7-3) = 10√(7-4) = 10√3

Product of Square Roots Calculator
Enter The Number Here Then Press The SUBMIT Button

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Roots - Learn What A Product Of Square Roots Is And How To Use The Square Roots Calculator

How Do We Compute The Product Of Square Roots?

Combined As Products?

Math Expression

Answer