The only way to simplify radicals is to take the radicand (the number under the radical) and split it into two factors, where one of them has to be a "perfect square"
A "perfect square" is a product of two of the same numbers
Example: 9 is a "perfect square" because 3*3=9
So, let's simplify and pull some numbers out of these radicals:
3sqrt(12) + 4sqrt(18) color(blue)(" Let's start with the left side"
3sqrt(4*3) + 4sqrt(18) color(blue)(" 4 is a perfect square")
3*2sqrt(3) + 4sqrt(18) color(blue)(" 4 is a perfect square, so take a 2 out")
6sqrt(3) + 4sqrt(18) color(blue)(" Simplify: "3*2=6," and leave the 3")
6sqrt(3) + 4sqrt(9*2) color(blue)(" 9 is a perfect square")
6sqrt(3) + 4*3sqrt(2) color(blue)(" 9 is a perfect square, so take a 3 out")
6sqrt(3) + 12sqrt(2) color(blue)(" Simplify: "4*3=12," and leave the 2")
color(red)(6sqrt(3) + 12sqrt(2))
Since sqrt(3) and sqrt(2) are different radicals, we can't add them, so we're done.
