https://file.aiquickdraw.com/mathbot/file/1726927377609xfmp7mwc.jpg

Let's solve the expression step by step:

The given expression is:
\[
3\sqrt{50} - \sqrt{8} + \sqrt{128} - 5\sqrt{18}
\]

### Step 1: Simplify each square root term.
- \( \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \)
- \( \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \)
- \( \sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2} \)
- \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \)

### Step 2: Substitute the simplified square roots back into the expression.
\[
3\sqrt{50} - \sqrt{8} + \sqrt{128} - 5\sqrt{18}
= 3(5\sqrt{2}) - 2\sqrt{2} + 8\sqrt{2} - 5(3\sqrt{2})
\]
This simplifies to:
\[
15\sqrt{2} - 2\sqrt{2} + 8\sqrt{2} - 15\sqrt{2}
\]

### Step 3: Combine like terms.
\[
(15\sqrt{2} - 15\sqrt{2}) + (8\sqrt{2} - 2\sqrt{2}) = 0 + 6\sqrt{2} = 6\sqrt{2}
\]

### Final Answer:
The simplified value of the expression is \( \boxed{6\sqrt{2}} \).

This matches option **e** in the provided answers.

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Do you have any further questions or need more details? Here are some related questions for practice:

1. Simplify \( 7\sqrt{75} - 4\sqrt{12} \).
2. Combine \( 2\sqrt{45} + 3\sqrt{20} - \sqrt{80} \).
3. Simplify \( 5\sqrt{72} - 2\sqrt{50} + \sqrt{18} \).
4. Solve \( \sqrt{200} - \sqrt{128} \).
5. Simplify \( \sqrt{32} + 4\sqrt{8} - 2\sqrt{18} \).

**Tip:** When simplifying square roots, try to factor out perfect squares to make the process easier!

Learn how to simplify the expression 3√50 - √8 + √128 - 5√18 by factoring and simplifying square roots. This problem covers key algebraic concepts, including addition and subtraction of square roots and radical simplification. Suitable for students in Grades 9-11.

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