Simplifying Algebraic Expressions: $\frac{1}{3} \sqrt{3} + \frac{1}{2} \sqrt{3}$
In this article, we will explore how to simplify the algebraic expression $\frac{1}{3} \sqrt{3} + \frac{1}{2} \sqrt{3}$. This expression involves the addition of two radical terms, and we will see how to combine them into a single term.
Step 1: Identify the Common Factor
The first step in simplifying this expression is to identify the common factor between the two terms. In this case, the common factor is $\sqrt{3}$.
Step 2: Rewrite the Expression
We can rewrite the expression as:
$\frac{1}{3} \sqrt{3} + \frac{1}{2} \sqrt{3} = \sqrt{3} \left( \frac{1}{3} + \frac{1}{2} \right)$
Step 3: Add the Coefficients
Next, we add the coefficients of the two terms:
$\frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}$
Step 4: Simplify the Expression
Finally, we can simplify the expression by combining the coefficients and the radical term:
$\frac{1}{3} \sqrt{3} + \frac{1}{2} \sqrt{3} = \sqrt{3} \left( \frac{5}{6} \right) = \frac{5\sqrt{3}}{6}$
Conclusion
In conclusion, the simplified form of the algebraic expression $\frac{1}{3} \sqrt{3} + \frac{1}{2} \sqrt{3}$ is $\frac{5\sqrt{3}}{6}$. By identifying the common factor, rewriting the expression, adding the coefficients, and simplifying the expression, we were able to combine the two radical terms into a single term.
