Question 708604
The two spheres each have their own radius. The large sphere may have r[b] and the small sphere may have radius r[s].  b for big, s for small.

{{{v=(4/3)*pi*r^3}}} for a sphere, volume.


You can treat your description like small sphere, v; large sphere, 2v.
You have
{{{v=(4/3)*pi*r[s]^3}}}  and   {{{2v=(4/3)*pi*r[b]^3}}}


Your goal was to compare the radius of the big sphere to the radius of the sphere of half the volume.  You could solve each of the above volume equations for r[s] and r[b], and then compare them.  


{{{r[s]=root(3,((3/(4*pi))v))}}} and {{{r[b]=root(3,((3/(4*pi))2v))}}}


You should factor those, like this:
{{{r[s]=root(3,3/(4*pi))*root(3,v)}}}  and  {{{r[b]=root(3,3/(4*pi))*root(3,2v)}}}.
even further,
{{{r[s]=root(3,3/(4*pi))*root(3,v)}}}  and  {{{r[b]=root(3,3/(4*pi))*root(3,v)*root(3,2)}}}.


When you look at the ratio of {{{r[b]}}} to {{{r[s]}}}, you will eliminate the root with the constants.  (cancelling as k/k=1).


To finally finish this, write the ratio of {{{r[b]}}} to {{{r[s]}}}.
{{{(r[b]/r[s])}}}=?what?