Question 244765
Old Stuff

Hint: Remember that {{{root(3,x)=(x)^(1/3)^""}}}. In addition, {{{sqrt(x)=(x)^(1/2)^""}}}. Use these two equations along with the identity {{{(x^y)^z=x^(yz)}}} to simplify the problem. Let me know if this hint helps or not. If not, then repost or ask me.


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New Stuff


{{{root(3,sqrt(5))}}} Start with the given expression.



{{{root(3,5^(1/2)^"")}}} Rewrite {{{sqrt(5)}}} as {{{5^(1/2)^""}}} using the property {{{sqrt(x)=(x)^(1/2)^""}}}



{{{(5^(1/2))^(1/3)}}} Convert {{{root(3,5^(1/2)^"")}}} to {{{(5^(1/2))^(1/3)}}} using the property {{{root(3,x)=(x)^(1/3)^""}}}



{{{5^((1/2)*(1/3))^""}}} Multiply the exponents using the idea that {{{(x^y)^z=x^(yz)}}}



{{{5^((1*1)/(2*3))^""}}} Combine the fractions.



{{{5^(1/6)^""}}} Multiply



{{{root(6,5)}}} Convert back to radical notation



So {{{root(3,sqrt(5))=root(6,5)}}}