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The question is based on the premise that It is not possible to simplify a radical without first factorising it. That is simply not true. Beginners may find it a useful step but that does not make it "important to always factor".

Simplifying radicals entails removing square factors of the radicand from under the radical. This can be done without factoring first.

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9y ago

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Can the radicand be negative when the index is even?

Given that the radicand is part of the question, not part of the answer, you can make the radicand whatever you want it to be. However, in any given root sum, for example, sqrt(-4), if the index is even, such as it is in a square root sum, the answer will always be positive. If the index is odd, and the radicand is negative, the answer will also be negative.


When simplifying an expression you a always b sometimes c never perform operations inside grouping symbols first?

A


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The rule of simplifying expressions involves combining like terms, applying the distributive property, and reducing fractions where possible. This process includes eliminating unnecessary parentheses, consolidating terms with the same variable or constant, and performing any arithmetic operations. The goal is to rewrite the expression in its simplest form while maintaining its value. Always ensure to follow the order of operations (PEMDAS/BODMAS) when simplifying.


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It depends on the circumstances. It is not always important


Why initiator efficiency in any free radical polymerization is always low?

Initiator efficiency in free radical polymerization is typically low because not all initiator molecules generate active radicals that are capable of initiating polymerization reactions. This is due to side reactions such as termination or chain transfer processes that can reduce the number of active radicals available for polymerization. Additionally, some radicals may not efficiently propagate the polymerization due to their reactivity or stability.


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The customer is always, always, right!


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I guess you mean "simplifying": Writing a term in a form that is deemed simpler (this is not always unique). For example, "4" is a simplification of "2+2", or "x^2" is a simplification of "(x-1)*(x+1)+1".


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No. If you are self-important, that is a negative.