Final answer:
The square root of a quotient equals the quotient of the square root of the numerator and denominator, which is choice (c). This follows the laws of exponents and can be used to simplify expressions involving square roots.
Step-by-step explanation:
The square root of a quotient equals the quotient of the square root of the numerator and denominator. This can be expressed mathematically as √(a/b) = √a / √b. Understanding this property helps when simplifying expressions involving square roots and when performing operations with exponents.
For example, let's consider the expression √(9/16). Using the property, we can take the square root of each, the numerator, and the denominator, separately, thus calculating √9 / √16, which equals 3/4. It's also aligned with the laws of exponents, where dividing exponents with the same base means you subtract the exponents, hence the square root is the exponent of 1/2. Therefore, (a^m) / (b^m) would be (a/b)^m, and for a square root, m equals 1/2.