Multiplication Property of Square and Cube  Roots

To indicate multiplication of square roots or of cube roots, we often write the radicals next to each other, without a multiplication dot between them.

For example,

When a radical is multiplied by a factor that does not contain a radical, we usually write the radical factor on the right.

For example,

To simplify a square-root radical or a cube-root radical, we often use these multiplication properties.

Property — The Multiplication Property of Square Roots and The Multiplication Property of Cube Roots English The root of a product is the product of the roots.
	Square Roots	Cube Roots
Algebra
Example	Here, a and b are nonnegative real numbers.	Here, a and b are real numbers.

These properties allow us to write a single radical as the product of two radicals. Sometimes we can simplify one (or both) of the radicals.

For example,

The property can also be used to write the product of two radicals as a single radical, provided the radicals have the same index.

For example,

Note:

The Multiplication Property applies only when the indices of the radicals are the same. So we cannot use it to multiply a square root by a cube root: