Question

The simplified form of $10\sqrt[3]{x} - 8\sqrt[3]{x}$ is
A.$18\sqrt[3]{x}$
B.$2\sqrt x $
C.$2\sqrt[3]{x}$
D.$18\sqrt x $

Answer 1

Hint: Identify the like terms and unlike terms and group them accordingly and simplify further. Like terms are the terms with the same variables and power.

Complete step-by-step answer:
Given that: $10\sqrt[3]{x} - 8\sqrt[3]{x}$
Here, there is a minus sign between the two terms and variables and its power both are the same.
Therefore, they are like terms and we can simplify them directly
$10\sqrt[3]{x} - 8\sqrt[3]{x}$
 $\begin{array}{l}
 = \sqrt[3]{x}(10 - 8)\\
 = \sqrt[3]{x}(2)\\
 = 2\sqrt[3]{x}
\end{array}$ (Taking variables common and simplify)
$10\sqrt[3]{x} - 8\sqrt[3]{x} = 2\sqrt[3]{x}$ is the required answer.
Therefore, option C is the correct option.
Additional Information: 1) The terms having the same variables and powers are known as the like terms. E.g. $x,4x,22x,45x$ are the like terms.
2) Terms which are not liked are called unlike terms.
E.g. $x,22,40y,300{x^2}$ are unlike terms.

Note: When grouping the terms,always observe the variables and its power and identify like terms and unlike terms and group them accordingly.When it is like terms it includes the terms with same power and variables