simplifying radical expressions

Do you mean (sqrt(6x))*(sqrt(18x^{2})? If so you can multiply thne two together under one sqrt.^{
}

So you get sqrt(6*18*x*x^{2}). Any perfect squares under the square root can be factored out. x^{2} is^{ }a perfect square so the square root of that is x and that comes out.

This gives you x * sqrt(6*18*x).

Let's see if we can factor out some perfect squares from 6*18. Breaking them both down we have

(3*2)*(3*3*2) = 3^{2} * 2^{2} * 3. The 3^{2} and 2^{2} become 3 and 2 when you factor them out. The other 3 stays under the square root.

So now our solution is 3*2*x*sqrt(3*x) = 6x * sqrt(3x)