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.




 

 Key Lesson Marker


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