square root of 6X times square root of 18X squared

Question

simplifying radical expressions

Answer 1

Do you mean (sqrt(6x))*(sqrt(18x²)? If so you can multiply thne two together under one sqrt.

So you get sqrt(6*18*x*x²). Any perfect squares under the square root can be factored out. x² 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) = 3² * 2² * 3. The 3² and 2² 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)