There are different means to multiply square roots in mathematics, it just simply depend on the format the question takes. A major topic where you can have to solve lot of these kinds of problem is Surd.
However, check out these steps to solve your square roots multiplication problems:
If the radicands are perfect square, you can actually find the square roots of the numbers separately, and multiply your result to obtain your final answer.
If the radicands are perfect square, and they are also the same number, then your answer would be the number. For example; √78× √78=78.
If the radicand are not perfect square, and probably not the same number too, just multiply the two numbers together. The result you get would still be having the radical sign. This might be your final answer.
You can solve the above step further by factoring out any perfect square in the radicand. The perfect square is solved, while the other number remain with the radical sign.