Questions: You were asked to combine the following radical expressions, if possible. sqrt(8 x^3) + 5 x sqrt(2 x) In the previous step, we determined that the first radical can be simplified as follows: sqrt(8 x^3) = 2 sqrt(2) * x sqrt(x) = 2 x sqrt(2 x) Notice that sqrt(2 x) is common to both terms, so we can combine both radical expressions. This gives us: 2 x sqrt(2 x) + 5 x sqrt(2 x) =

You were asked to combine the following radical expressions, if possible.

sqrt(8 x^3) + 5 x sqrt(2 x)

In the previous step, we determined that the first radical can be simplified as follows:

sqrt(8 x^3) = 2 sqrt(2) * x sqrt(x) = 2 x sqrt(2 x)

Notice that sqrt(2 x) is common to both terms, so we can combine both radical expressions. This gives us:

2 x sqrt(2 x) + 5 x sqrt(2 x) =
Transcript text: My Apps Dashboard | Coastal Pin Content / MATH1111: College Alg $\times$ Tutor - Step by Step Page 2 of 21 https//learn.hawkeslearning.com/Portal/Lesson/lesson_practice\# Question 8 of 24, Step 1 of 1 5/24 Correct Tutor You were asked to combine the following radical expressions, if possible. \[ \sqrt{8 x^{3}}+5 x \sqrt{2 x} \] In the previous step, we determined that the first radical can be simplified as follows: \[ \sqrt{8 x^{3}}=2 \sqrt{2} \cdot x \sqrt{x}=2 x \sqrt{2 x} \] Notice that $\sqrt{2 x}$ is common to both terms, so we can combine both radical expressions. This gives us: $\square$ \[ 2 x \sqrt{2 x}+5 x \sqrt{2 x}= \] Back to Practice Previous Page
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Solution

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Solution Steps

Step 1: Simplify the first radical expression

The first radical expression is given as: \[ \sqrt{8 x^{3}} \] We simplify it as follows: \[ \sqrt{8 x^{3}} = \sqrt{4 \cdot 2 \cdot x^{2} \cdot x} = \sqrt{4} \cdot \sqrt{2} \cdot \sqrt{x^{2}} \cdot \sqrt{x} = 2 \cdot \sqrt{2} \cdot x \cdot \sqrt{x} = 2x \sqrt{2x} \]

Step 2: Identify the common term

Both terms in the expression \(2x \sqrt{2x} + 5x \sqrt{2x}\) share the common term \(\sqrt{2x}\).

Step 3: Combine the terms

Since both terms have the common factor \(\sqrt{2x}\), we can combine them by adding their coefficients: \[ 2x \sqrt{2x} + 5x \sqrt{2x} = (2x + 5x) \sqrt{2x} = 7x \sqrt{2x} \]

Final Answer

\(\boxed{7x \sqrt{2x}}\)

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