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I am having problems understanding how to multiply radicals i.e (($√5 )(^3√2)$). I know the answer is $ ^6√500 $. I just do not understand how to get there.

Update: I've solidified my understanding of this question but my current methodology leads me to -> (125^(3/6))(4^(2/6)). Which leads me to the answer -> $ ^6√500^5 $.

What am i doing wrong to lead me to this answer with the extra exponent of $ ^5 $

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Since $\sqrt{5} = 5^{1/2} = (5^3)^{1/6}$ and $\sqrt[3]{2} = 2^{1/3} = (2^2)^{1/6}$, we get $\sqrt{5}\sqrt[3]{2} = (5^3)^{1/6}(2^2)^{1/6} = 500^{1/6} = \sqrt[6]{500}$.

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  • $\begingroup$ Thank You! looking at the step by step helped me understand my problem and how to solve it. $\endgroup$
    – foo
    Commented May 13, 2014 at 1:37

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