Multiply $2.3$ and $\frac{1}{100000}$ to get $\frac{23}{1000000}$.
$$\sqrt{\frac{\frac{23}{1000000}}{0.08}}$$
Express $\frac{\frac{23}{1000000}}{0.08}$ as a single fraction.
$$\sqrt{\frac{23}{1000000\times 0.08}}$$
Multiply $1000000$ and $0.08$ to get $80000$.
$$\sqrt{\frac{23}{80000}}$$
Rewrite the square root of the division $\sqrt{\frac{23}{80000}}$ as the division of square roots $\frac{\sqrt{23}}{\sqrt{80000}}$.
$$\frac{\sqrt{23}}{\sqrt{80000}}$$
Factor $80000=200^{2}\times 2$. Rewrite the square root of the product $\sqrt{200^{2}\times 2}$ as the product of square roots $\sqrt{200^{2}}\sqrt{2}$. Take the square root of $200^{2}$.
$$\frac{\sqrt{23}}{200\sqrt{2}}$$
Rationalize the denominator of $\frac{\sqrt{23}}{200\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
