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What’s the definition of simplest radical form a mathematical expression, indicating a route by means of a radical sign. A rule for dividing square root stating that you Rison may be applied independently to the numerator of the denominator or to the quotient of the reticent. Rule stating that a radical may be applied to the individual factors of the reticent. The quantity under a radical sign. A factor of a number that wins squared gives the number. A square root that has perfect square factors and its radicals. A number of tamed from squaring and integer multiplying a number by itself. Radicals with the same index and radicand

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The terms you're asking about seem to be related to various concepts in radical expressions and square roots. Here's a breakdown of the definitions:

  1. Simplest Radical Form: A radical expression is in simplest radical form when there are no perfect square factors (other than 1) left under the radical sign. This means that the radical has been simplified as much as possible.

  2. Division of Square Roots Rule: This rule states that the square root of a quotient can be expressed as the quotient of the square roots: \(\sqrt{a/b} = \sqrt{a} / \sqrt{b}\).

  3. Multiplication of Radicals Rule: This rule states that the product of square roots can be expressed as the square root of the product: \(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\).

  4. Radicand: The radicand is the quantity (the number or expression) under the radical sign. For example, in \(\sqrt{a}\), \(a\) is the radicand.

  5. Square Root: A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, since \(3 \times 3 = 9\).

  6. Perfect Square Factors: These are the factors of a number that are perfect squares (like 1, 4, 9, 16, etc.) and that can be taken out of the radical sign when simplifying.

  7. Radicals with the Same Index and Radicand: These are radicals that have the same root. For example, \(\sqrt{2}\) and \(\sqrt{2}\) or \(\sqrt[3]{x}\) and \(\sqrt[3]{x}\) are like radicals.

If you need more specific definitions or examples related to any of these concepts, feel free to ask!