Factoring the Radicand
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Factoring the Radicand
Factors of the radicand can be rewritten as separate radicals with the same index. For example, \(\sqrt{14} = \sqrt{2\cdot 7} = \sqrt{2} \cdot \sqrt{7}\) or \(\sqrt[{4}]{55} = \sqrt[{4}]{5 \cdot 11} = \sqrt[{4}]{5} \cdot \sqrt[{4}]{11}\). This is important when simplifying radicals.
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Factoring the Radicand
\(\sqrt[{n}]{a \cdot b} = \sqrt[{n}]{a} \cdot \sqrt[{n}]{b} \)
where \(n\) is the index, and \(a\) and \(b\) are factors of the radicand
where \(n\) is the index, and \(a\) and \(b\) are factors of the radicand