Answer
$$5\sqrt {2}$$
Work Step by Step
According to the product rule for square roots, the square root of two radicals that are multiplied together is the product of the two radicands.
In this problem, we first multiply the two radicands together to get one radical expression:
$$\sqrt {10} \times \sqrt {5} = \sqrt {50}$$
We can now simplify by using the product rule for square roots to split the radical into two component radicals. We want to divide the radical expression so that the radicand is the product of one perfect square and another factor:
$$\sqrt {50} = \sqrt {25 \times 2}$$
Now we take the square root of $25$, which is $5$:
$$5\sqrt {2}$$
