In my previous post,<\/a> I mentioned how simplifying the square root of a variable to a power is slightly different from simplifying the square root of a number. Let’s review quickly:<\/p>\n Example 1: Simplify √48<\/strong><\/p>\n Solution:<\/p>\n Step 1: Factor 48 into the biggest perfect square that goes into it, times the number it goes in:<\/p>\n 48=16×3 so √48=√16√3<\/p>\n Step 2: Take the square root of 16.<\/p>\n √48=4√3.<\/p>\n Example 2: Simplify √x21<\/sup><\/strong><\/p>\n Solution:<\/p>\n Step 1: Realize that √x21<\/sup>=√x20<\/sup>√x<\/p>\n Step 2: Realize that √x20<\/sup>=x10<\/sup> (Since x10<\/sup>x10<\/sup>=x20<\/sup>)<\/p>\n Therefore, √x21<\/sup>=√x20<\/sup>√x=x10<\/sup>√x<\/p>\n Now, let’s perform the two processes side by side:<\/p>\n Example 3: Simplify √28x15<\/sup>y8<\/sup><\/strong><\/p>\n Step 1: First, separate the radical into a convenient product.<\/p>\n √28x15<\/sup>y8<\/sup>=√28√x15<\/sup>√y8<\/sup><\/p>\n Step 2: Tackle each part separately.<\/p>\n 28=4×7; x15<\/sup>=x14<\/sup>x;<\/p>\n √28√x15<\/sup>√y8<\/sup>=√4√7√x14<\/sup>√x√y8<\/sup>=(2√7)(x7<\/sup>√x)(y4<\/sup>)<\/p>\n Step 3: Recollect all the simplified terms to the front.<\/p>\n (2√7)(x7<\/sup>√x)(y4<\/sup>)=2x7<\/sup>y4<\/sup>√7x<\/p>\n Terms that have been “rooted out” go in front of the radical so that they are clearly not in it. The terms behind a radical sign are meant to be in it. Such is the convention used almost universally in the math world.<\/p>\n