https://file.aiquickdraw.com/mathbot/file/17272004539618z44z841.jpg

The problem shown in the image asks to simplify the square root of 63, or \( \sqrt{63} \).

To simplify this:

1. First, find the prime factors of 63:
   \[
   63 = 3^2 \times 7
   \]

2. Now, rewrite the square root:
   \[
   \sqrt{63} = \sqrt{3^2 \times 7} = \sqrt{3^2} \times \sqrt{7} = 3\sqrt{7}
   \]

Thus, the simplified form of \( \sqrt{63} \) is \( 3\sqrt{7} \).

Would you like more details on this? Here are some related questions:

1. How do you simplify square roots of non-perfect squares?
2. What are prime factorization methods for large numbers?
3. How do square roots behave under multiplication?
4. How can you approximate non-perfect square roots like \( \sqrt{7} \)?
5. What are common mistakes when simplifying radicals?

**Tip:** When simplifying square roots, always look for perfect square factors.

Learn how to simplify the square root of 63 using prime factorization. This solution involves breaking down 63 into 3^2 × 7 and applying square root rules. Suitable for students in Grades 8-10.

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