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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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Q: Why is it important to always factor the radicand first when simplifying radicals?
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