Multiply Radicals

In this problem, we need to multiply two radicals: the square root of six times negative three square root of eight.

Let's first write down the expression and identify the coefficients and the radicands.

We can group the coefficients together and the radicals together. Note that the square root of six has an invisible coefficient of one.

Multiplying the coefficients, one times negative three gives us negative three. According to the product rule for radicals, we can multiply the numbers inside the square roots together.

Six times eight is forty-eight. So we have negative three times the square root of forty-eight.

Now, we need to simplify the square root of forty-eight. We search for the largest perfect square factor of forty-eight, which is sixteen.