https://file.aiquickdraw.com/mathbot/file/1726109411058sho1ux7r.jpg

The expression in the image is:

\[
4\sqrt{200} - 2\sqrt{242} - 5\sqrt{60} + 10\sqrt{2}
\]

Let's simplify it step by step.

### Step 1: Simplify the square roots

- \(\sqrt{200} = \sqrt{2^2 \cdot 5^2} = 10\sqrt{2}\)
- \(\sqrt{242} = \sqrt{2 \cdot 121} = 11\sqrt{2}\)
- \(\sqrt{60} = \sqrt{2^2 \cdot 15} = 2\sqrt{15}\)
- \(\sqrt{2}\) remains as it is.

### Step 2: Substitute back into the expression
\[
4\sqrt{200} = 4 \cdot 10\sqrt{2} = 40\sqrt{2}
\]
\[
2\sqrt{242} = 2 \cdot 11\sqrt{2} = 22\sqrt{2}
\]
\[
5\sqrt{60} = 5 \cdot 2\sqrt{15} = 10\sqrt{15}
\]
\[
10\sqrt{2} = 10\sqrt{2}
\]

Now, the expression becomes:
\[
40\sqrt{2} - 22\sqrt{2} - 10\sqrt{15} + 10\sqrt{2}
\]

### Step 3: Combine like terms

The terms with \(\sqrt{2}\) can be combined:
\[
(40 - 22 + 10)\sqrt{2} = 28\sqrt{2}
\]

So, the simplified expression is:
\[
28\sqrt{2} - 10\sqrt{15}
\]

That is the final simplified form.

Would you like more details or further clarification?

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Here are five related questions for further exploration:
1. What is the process for simplifying radicals with prime factorization?
2. How can you recognize perfect square factors inside square roots?
3. How would the expression change if the coefficients were negative?
4. What are some real-world applications of simplifying radical expressions?
5. How do operations like addition and subtraction work with radical terms?

**Tip:** Always look for common factors within square roots when simplifying to make calculations easier.

Sederhanakan ekspresi berikut: 4√200 - 2√242 - 5√60 + 10√2

Learn how to simplify the radical expression 4√200 - 2√242 - 5√60 + 10√2 with step-by-step instructions. This problem covers key concepts like simplifying square roots and combining like terms, making it suitable for students in Grades 9-11.

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