Quotient 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 quotient property of square roots states that the square root of a fraction (or quotient) is equal to the square root of the numerator divided by the square root of the denominator. Mathematically, it is expressed as:
This property allows you to simplify square roots of fractions by taking the square roots of the numerator and denominator separately.
Example:
This property is helpful when simplifying expressions involving square roots of fractions, especially when both the numerator and denominator are perfect squares.
Important Note:
The quotient property applies when both the numerator and denominator are non-negative numbers, since square roots of negative numbers are not real numbers in Algebra 1.