Wang Clark
11/23/2023 · Middle School
3. What is the simplest form of the sum \( -2 x \sqrt{6 x}+5 x \sqrt{6 x}, x \geq 0 \) ? \( \begin{array}{ll}\text { A } 3 \sqrt{6 x} & \text { B } 6 \sqrt{12 x} \\ \text { C } 3 x \sqrt{6 x} & \text { D } 6 x \sqrt{12}\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( -2 x \sqrt{6 x} + 5 x \sqrt{6 x} \), we can first factor out the common term \( x \sqrt{6 x} \).
1. Identify the common factor:
\[
-2 x \sqrt{6 x} + 5 x \sqrt{6 x} = (5 - 2) x \sqrt{6 x}
\]
2. Simplify the coefficients:
\[
(5 - 2) x \sqrt{6 x} = 3 x \sqrt{6 x}
\]
Thus, the simplest form of the sum is:
\[
3 x \sqrt{6 x}
\]
Now, let's compare this with the given options:
- A: \( 3 \sqrt{6 x} \)
- B: \( 6 \sqrt{12 x} \)
- C: \( 3 x \sqrt{6 x} \)
- D: \( 6 x \sqrt{12} \)
The correct answer is:
\[
\boxed{3 x \sqrt{6 x}}
\] (Option C)
Quick Answer
The simplest form is \( 3 x \sqrt{6 x} \).
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