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Product Property of Square Roots
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The product property of square roots states that the square root of a product is equal to the product of the square roots of the individual factors. In other words:
sqrt(a • b) = sqrt(a) • sqrt(b)
This property allows you to simplify square roots by breaking them up into smaller parts. For example:
sqrt(12) = sqrt(4 • 3) = sqrt(4) • sqrt(3) = 2sqrt(3)
This property is helpful for simplifying expressions involving square roots, especially when the radicand (the number inside the square root) can be factored into smaller, more manageable parts.
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