When I teach my students to simplify radicals, I encourage them to factor out the greatest perfect square, although there are certainly merits to teaching them to do a complete factor tree. One advantage of having them factor out the greatest perfect square is that the students become familiar with the properties of square roots of positive numbers, (such as the square root of a product equals the product of the square roots), which come in handy later on in their math careers.
I use this worksheet for my algebra and geometry students before we use the Pythagorean Theorem.
The preview file is a pdf so you can see exactly what you're getting; the product file is a word document, which you may edit for your students.
keywords: simplifying radicals, perfect square, radicals, Jonnard