Step Troot

Let $f,g$ and $h$ be positive numbers satisfying $f + g + h = \dfrac{100 \sqrt t}{27}$ and $(fg+gh+hf)\left(\dfrac { 2h }{ g+9f } +\dfrac { 2g }{9 h+f } +\dfrac { 2f }{ h+9g } \right)\ge 102030$ .

Find the least possible value of $\lfloor \sqrt t \rfloor$ .