You can evaluate inside a held expression with replacement rules:
TeXForm[HoldForm[Sqrt[sqrtRad]]] /.
sqrtRad -> Round[RandomReal[{1, 10000}], .01]
or with With:
With[{sqrtRad = Round[RandomReal[{1, 10000}], .01]},
TeXForm[HoldForm[Sqrt[sqrtRad]]]]
or, more mysteriously, this way:
sqrtRad = Round[RandomReal[{1, 10000}], .01];
With[{sqrtRad = sqrtRad},
TeXForm[HoldForm[Sqrt[sqrtRad]]]]
There are probably other ways.