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

Solution:

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.

√48=4√3.

Example 2: Simplify √x²¹

Solution:

Step 1: Realize that √x²¹=√x²⁰√x

Step 2: Realize that √x²⁰=x¹⁰ (Since x¹⁰x¹⁰=x²⁰)

Therefore, √x²¹=√x²⁰√x=x¹⁰√x

Now, let’s perform the two processes side by side:

Example 3: Simplify √28x¹⁵y⁸

Step 1: First, separate the radical into a convenient product.

√28x¹⁵y⁸=√28√x¹⁵√y⁸

Step 2: Tackle each part separately.

28=4×7; x¹⁵=x¹⁴x;

√28√x¹⁵√y⁸=√4√7√x¹⁴√x√y⁸=(2√7)(x⁷√x)(y⁴)

Step 3: Recollect all the simplified terms to the front.

(2√7)(x⁷√x)(y⁴)=2x⁷y⁴√7x

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.