The principle that allows the division of radicals before simplifying is called the "Product and Quotient Property of Radicals." This principle states that the square root (or any nth root) of a quotient can be expressed as the quotient of the square roots (or nth roots). In mathematical terms, for any non-negative numbers \(a\) and \(b\) (with \(b \neq 0\)):
\[ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \]
This property applies similarly to nth roots. This principle is useful when simplifying expressions involving radicals.
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