To simplify the given expression:
$$\sqrt{\frac{(0.0023\cdot750)}{(0.00345\cdot1.25)}}$$
We can first simplify the expression inside the square root by multiplying the numerators and denominators:
$$\sqrt{\frac{0.0023\cdot750}{0.00345\cdot1.25}} = \sqrt{\frac{1.725}{0.0043125}}$$
Then we can divide the numerator and denominator by 0.0043125 to get:
$$\sqrt{\frac{1.725}{0.0043125}} = \sqrt{400} = 20$$
Therefore, the simplified expression is 20.