Question 623092
I assume by "root symbol" you mean square root. (In the future, please specify which kind of root.) I also assume that "13a2b"  means {{{13a^2*b}}}<br>
There are several ways to deal with a fraction of square roots. My prefernce is to do the following:<ol><li>Use the {{{root(a, p)/root(a, q) = root(a, p/q )}}} property to join the two square roots into one.</li><li>Reduce the fraction. (Note: If you're clever you will keep in mind step 3 and maybe not reduce the fraction as fully as possible. For example, if you had {{{sqrt(2/4)}}} then you would not reduce the fraction because step 3 wants perfect square denominators. 4 is already a perfect square. If we reduce 2/4 to 1/2 then we would no longer have a perfect square denominator. And we would end up changing 1/2 back to 2/4 in step 3.)</li><li>If there still is a denominator, then make sure it is a perfect square.</li><li>If there still is a denominator, then use the {{{sqrt(p)/sqrt(q) = sqrt(p/q)}}} property again, this time in the other direction -- to split the numerator from the denominator.</li><li>Simplify any remaining square roots and fractions.</li></ol>Let's see this in action:
{{{sqrt(39a^3b^5)/sqrt(13a^2*b)}}}
1. Join the square roots:
{{{sqrt((39a^3b^5)/(13a^2*b))}}}
2. Reduce the fraction (maybe not fully).
The entire denominator cancels out leaving:
{{{sqrt((3ab^4)/1)}}}
or just
{{{sqrt(3ab^4)}}}
3. If there's a still denominator, ...
There is no denominator.
4. If there's a still denominator, ...
There is no denominator.
5. Simplify any remaining square roots and fractions.
To simplify a square root, look for perfect square factors of the radicand (the expression inside). There are not prefect square factors in the 3 or the a. But there are perfect square factors in {{{b^4}}}. When I factor out the perfect squares I like to put those factors in front:
{{{sqrt(b^2*b^2*3a)}}}
Then you use another property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}}, split the square root so that eah perfect square factor is in its own square root:
{{{sqrt(b^2)*sqrt(b^2)*sqrt(3a)}}}
The square roots of the perfect squares simplify:
{{{b*b*sqrt(3a)}}}
which simplifies to:
{{{b^2*sqrt(3a)}}}