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When you see a cube root, it means you are looking for a number that, when multiplied by itself three times, gives you the original number inside the root. For instance, if you have \(\text{鲁鈭�8}\), you are looking for a number that when multiplied by itself three times results in 8. That number is 2, because \({2 \times 2 \times 2 = 8}\).
Now, let's think about cube roots with variables. If you have \(\text{鲁鈭歺鲁}\), it simplifies to x because \({x \times x \times x = x鲁}\).
Let's look at one from the solution: \(\text{鲁鈭�6x鈦磢\). First, we break it down: the cube root of 6 and the cube root of \({x鲁 \times x}\). The cube root of \({x鲁}\) is x, so you get \({x \text{鲁鈭�6x}}\).
Similarly, for \(\text{鲁鈭�48x}\), you can factor out an 8, because \(\text{鲁鈭�8}\) is 2. This gives \(- 2 \text{鲁鈭�6x}\).
Combining these terms becomes easy if they share the same radicand (inside the root part).

Combining like terms is a fundamental skill in algebra. It helps to make expressions simpler. Like terms are terms that have the same variables raised to the same power.
For example, \({x鲁}\) and \({2x鲁}\) are like terms because they both have \({x鲁}\). But, \({x鲁}\) and \({x虏}\) are not, because the exponents are different.
The term 'like terms' also applies to radical expressions. For instance, if you have \({5 \text{鲁鈭�6x}}\) and \({- \text{虏鲁鈭�6x}}\), they are like terms, because they both include \({\text{鲁鈭�6x}}\).
The key is that the radicand (the part inside the root) must be identical.
In our problem, both \({x \text{鲁鈭�6x}}\) and \({- 2 \text{鲁鈭�6x}}\) have the same radicand, \({\text{鲁鈭�6x}}\), making them like terms. So you can combine them like this: \({x \text{鲁鈭�6x} - 2 \text{鲁鈭�6x}}\), which simplifies to \({(x - 2) \text{鲁鈭�6x}}\).

Simplifying radical expressions lets you turn complex expressions into simpler ones, making them easier to understand and work with.
Here鈥檚 how you can simplify a radical expression step-by-step:

• First, handle any factorable numbers or variables inside the radical. Factorize them.
• Identify perfect cubes (for cube roots) or squares (for square roots) inside the radical and simplify those.
• Combine any results properly if they share the same radicand.

By following these steps, you reduce the radical expression into its simplest form.
For example, \(\text{鲁鈭�6x鈦磢\) can be factored into \({x \text{鲁鈭�6x}}\) by recognizing \({x鲁}\) inside the root.
By simplifying both individual terms in the original problem, you make it possible to combine them more easily because they now share the same radicand.