Question 244805
{{{root(5,sqrt(3))}}} Start with the given expression.



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



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



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



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



{{{3^(1/10)^""}}} Multiply



{{{root(10,3)}}} Convert back to radical notation



So {{{root(5,sqrt(3))=root(10,3)}}}