Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

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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
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,


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: