Solving a Radical Equation

MathematicsRadical EquationsMedium

Published: April 28, 2026

Question

8. $3\sqrt[4]{2x-4} + 2 = 8$

Animated Video Solution

The first half plays free, the full solution is in the app.

Step 1

Let's solve this radical equation for x. The problem is three times the cube root of two x minus four, plus two equals eight.

Step 2

Our first goal is to isolate the cube root term. Let's start by subtracting two from both sides of the equation.

3\sqrt[3]{2x - 4} + 2 = 8

Step 3

When we subtract two from eight, we are left with six on the right side.

Step 4

So, three times the cube root of two x minus four equals six.

Step 5

Next, we divide both sides by three to further isolate the cube root.

Step 6

Six divided by three is simply two. Now we have the cube root of two x minus four equals two.

Step 7

To eliminate the cube root, we need to cube both sides of the equation.

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