This worksheet is designed to replace a lecture on the topic of simplifying radicals. I advocate that students find the biggest perfect square factor that divides evenly into the given number. (I tell them: it divides in a whole number of times). The "cost" of this approach is that it's not the simplest way to do it, so it takes students a longer time, but they reinforce their mental arithmetic, they become more proficient in working with perfect squares, and they become familiar with the properties of square roots, at least in my experience.
I start out class with a 10-minute "mini-lesson," giving my students some basic examples of what today's lesson will be about, such as simplifying the square root of 12 (2 root 3), the square root of 64 ("boring" 8), and the square root of 30 (already simplified, since the biggest perfect square is 1). I also tie these ideas to the idea of simplifying fractions: you can "simplify" a fraction such as 10/20 down to 5/10, but you're not really "done" until you factor out the biggest factor that divides into 10 and 20 evenly.
Once the mini-lesson is over, I have them get to work within their groups on this worksheet.
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
This worksheet is intended to be written on directly.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.
Immediately before this worksheet, I use the worksheet named 'Geometry Angle Puzzle Spring 2014' (http://www.teacherspayteachers.com/Product/Geometry-Angle-Puzzle-Spring-2014-1266635
), and immediately after this worksheet, I use the worksheet named 'Ratios Proportions and the Geometric Mean Spring 2014' (http://www.teacherspayteachers.com/Product/Ratios-Proportions-and-the-Geometric-Mean-Spring-2014-1266682