Tutoring math, simplifying radicals constitutes one of the most difficult topics for high school students. The math tutor offers a step-by-step approach which continues here.
In my previous post, 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:
Example 1: Simplify √48
Step 1: Factor 48 into the biggest perfect square that goes into it, times the number it goes in:
48=16×3 so √48=√16√3
Step 2: Take the square root of 16.
Example 2: Simplify √x21
Step 1: Realize that √x21=√x20√x
Step 2: Realize that √x20=x10 (Since x10x10=x20)
Now, let’s perform the two processes side by side:
Example 3: Simplify √28x15y8
Step 1: First, separate the radical into a convenient product.
Step 2: Tackle each part separately.
Step 3: Recollect all the simplified terms to the front.
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.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.