Having the following product:
![(\sqrt[]{5x})\cdot(\sqrt[]{x+3})](https://img.qammunity.org/2023/formulas/mathematics/college/eai1fozqt0qyb1qx5bzerzr9liahqa86mg.png)
We need to establish the values of x for which it is defined.
The product has 2 square roots. We know that square roots are defined in real numbers only when its argument is 0 or a positive number.
We can begin checking the first one: √(5x). The argument of the square root (5x) has to be equal or larger than 0, then:

We can divide both sides by 5, having:

The first factor is defined for values of x larger or equal to 0.
Following the same logic for the other factor:

Then, we have two restrictions so far:

The restrictions for the product of both radicals will be the intersection of the two previous conditions. The first restriction goes from 0 to infinity and the second one from -3 to infinity. The intersection of both intervals gives the numbers from 0 to infinity. Then, the values of x for which the product is defined are:

Correct option is D.