Simplify the following expression: 2√3 + √3 - 5√3
Understand the Problem
The question requires simplifying an expression involving square roots. We need to combine terms with the same radical, in this case, (\sqrt{3}). We will add and subtract the coefficients of the radical to arrive at a simplified expression.
Answer
$-2\sqrt{3}$
Answer for screen readers
$-2\sqrt{3}$
Steps to Solve
- Identify like terms
In the expression $2\sqrt{3} + \sqrt{3} - 5\sqrt{3}$, all terms contain $\sqrt{3}$, so they are like terms.
- Combine the coefficients
Add and subtract the coefficients of the $\sqrt{3}$ terms: $2 + 1 - 5 = 3 - 5 = -2$
- Write the simplified expression
Combine the result from step 2 with the radical $\sqrt{3}$ to get the simplified expression: $-2\sqrt{3}$
$-2\sqrt{3}$
More Information
The expression is now in its simplest form because the radical $\sqrt{3}$ cannot be simplified further, and there are no more like terms to combine.
Tips
A common mistake is to try to combine terms that don't have the same radical. For example, you cannot directly add $\sqrt{2}$ and $\sqrt{3}$. Also, be careful with the signs when adding and subtracting the coefficients.
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