Question 1042643
sqrt(13) is somewhere, {{{3<sqrt(13)<4}}}.  Find it any way you need to.


{{{9<13<16}}};
{{{system(3.3^2=10.89,3.4^2=11.56,3.5^2=12.25,3.6^2=12.96,3.7^2=13.69)}}}
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{{{system(3.62^2=13.1044,13.61^2=13.0321)}}}
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sqrt(13) is somewhere between 3.6 and 3.61.


Using a calculator will give, to six figures,  {{{3sqrt(13)=10.8167}}}.


NOTE:  I misread your problem.  You wanted CUBED root of {{{3*sqrt(13)}}}.
You would really more be able to use {{{root(3,3sqrt(13))}}} to be between {{{root(3,8)}}} and {{{root(3,27)}}}  to help find it in similar fashion.
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About 2.21154