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To simplify the expression \( \sqrt{2} - 3\sqrt{45} + 3\sqrt{45} \), we need to follow these steps:

1. **Combine Like Terms:** Notice that the terms \(-3\sqrt{45}\) and \(3\sqrt{45}\) are like terms because they have the same radical part. When combined, they cancel each other out:
   \[ -3\sqrt{45} + 3\sqrt{45} = 0 \]

2. **Simplify the Expression:** With the like terms canceled out, the simplified expression is just \( \sqrt{2} \).

So the simplified expression is \( \sqrt{2} \). The correct answer from the options provided is the one that corresponds to \( \sqrt{2} \).

Would you like further explanation or details on any part of this solution?

Here are some questions you might want to explore next:
1. How do you simplify radicals?
2. What are the rules for combining like terms in radical expressions?
3. How do you rationalize the denominator of a fraction?
4. What is the process for simplifying expressions with multiple radicals?
5. How do you add and subtract radical expressions?

**Tip:** When simplifying expressions involving radicals, always look for like terms and consider whether you can simplify the radicals themselves.

Learn how to simplify the radical expression √2 - 3√45 + 3√45 step-by-step. This problem covers radicals and combining like terms, showing how to simplify expressions effectively. Suitable for high school students.

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