# How do you multiply radical expressions with different indices?

Mar 22, 2015

Make the indices the same (find a common index).

Example: $\sqrt{5} \cdot \sqrt[3]{2}$

The common index for 2 and 3 is the least common multiple, or 6

$\sqrt{5} = \sqrt[6]{{5}^{3}} = \sqrt[6]{125}$

$\sqrt[3]{2} = \sqrt[6]{{2}^{2}} = \sqrt[6]{4}$

So
$\sqrt{5} \cdot \sqrt[3]{2} = \sqrt[6]{125} \sqrt[6]{4} = \sqrt[6]{125 \cdot 4} = \sqrt[6]{500}$

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