Basic Square Root Question

I was reading an article on Purplemath about simplifying the square root terms. For instance in they instruct users to break down as a product and simply from there .

However what if you used a different pair of factors? Such as ? I understand once you get a perfect square you can remove it from under the radicand, but I attempted this problem and could not figure it out with the pair of factors I have. etc

I understand that we could simply solve by

knowing but that defeats the purpose of this exercise.