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Fourth roots might sound a little complicated at first, but it's simpler than you think! Just like square roots (where you find a number that, when multiplied by itself, equals the original number), fourth roots involve finding a number that, when multiplied by itself four times, equals the given number. For example, if we have \(y^4 = 16\), finding the fourth root of both sides can be written as \(y = \pm \sqrt[4]{16}\). This means we're looking for a number that, when used as a factor four times, results in 16.

In simpler terms, \sqrt[4]{16}\ means:

• \(2 \times 2 = 4 \) and
• \(4 \times 2 = 8 \) and finally
• \(8 \times 2 = 16 \).

So, \sqrt[4]{16}\ equals 2.

And because the root can be both positive and negative (since \(-2 \times -2 \times -2 \times -2 = 16)\), the number 2 satisfies this condition, and both \(y = 2\) and \y = -2\ are valid solutions.

When solving any equation, one of the crucial steps is to first 'isolate' the term containing the variable. This means you want to get the variable alone on one side of the equation, so you can solve for it more easily.

Let's look at our example \(3y^4 = 48\).
First, we need to divide both sides of the equation by 3 to get \y^4\ by itself:

• \(\frac{3y^4}{3} = \frac{48}{3} \)
• resulting in \(y^4 = 16\).

This step is crucial because it simplifies the equation and prepares it for the next steps, such as taking roots or applying other mathematical operations. Always remember this principle: isolate the variable term to make solving easier and clearer.

In math, a 'real solution' refers to a number that can be found on the number line. These numbers can be positive, negative or zero, and do not include imaginary or complex numbers.

When isolating and solving our equation, we find \(y^4 = 16\).
The fourth root gives us two real solutions: \(y = 2\) and \(y = -2\). These are both real numbers because they exist on the number line.


Not all equations will have real solutions, but in this specific problem, we do! When you solve polynomial equations, always check if the solutions you find are real numbers. This will help verify if your answer makes sense in the context of the original problem.