To simplify the square root of 349, let's follow these steps:

1. **Check if 349 is a perfect square**: First, check whether 349 is a perfect square by finding the square root of 349. Since \( \sqrt{349} \) is not an integer, 349 is not a perfect square.

2. **Check for factors**: We look for factors of 349 that are perfect squares. If we factorize 349, we find that it is a prime number, which means it has no factors other than 1 and 349.

Since 349 is a prime number and has no perfect square factors, \( \sqrt{349} \) cannot be simplified further.

Thus, the simplified form of \( \sqrt{349} \) is simply \( \sqrt{349} \).

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If you have any questions or need further details, feel free to ask!

Here are some related questions:

1. How do you simplify square roots of non-prime numbers?
2. What are perfect square numbers?
3. How do you estimate the value of \( \sqrt{349} \) without a calculator?
4. What is the process for simplifying square roots involving variables, such as \( \sqrt{4x^2} \)?
5. Can all square roots be simplified?

**Tip**: For non-perfect square roots, always check if the number can be factored into a product involving a perfect square!

Learn how to simplify the square root of 349 with a detailed step-by-step guide. Understand why 349 is not a perfect square and how prime numbers affect the simplification of square roots. Suitable for students in Grades 7-9.

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