# 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 √x ^{21}**

Solution:

Step 1: Realize that √x^{21}=√x^{20}√x

Step 2: Realize that √x^{20}=x^{10} (Since x^{10}x^{10}=x^{20})

Therefore, √x^{21}=√x^{20}√x=x^{10}√x

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

**Example 3: Simplify √28x ^{15}y^{8}**

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

√28x^{15}y^{8}=√28√x^{15}√y^{8}

Step 2: Tackle each part separately.

28=4×7; x^{15}=x^{14}x;

√28√x^{15}√y^{8}=√4√7√x^{14}√x√y^{8}=(2√7)(x^{7}√x)(y^{4})

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

(2√7)(x^{7}√x)(y^{4})=2x^{7}y^{4}√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.