https://file.aiquickdraw.com/mathbot/file/1726451417517ahukxzs6.jpg

The expression in the image is \( \sqrt{63} \). 

To simplify \( \sqrt{63} \), we break it down into prime factors:

\[
63 = 9 \times 7 = 3^2 \times 7
\]

So, \( \sqrt{63} \) can be rewritten as:

\[
\sqrt{63} = \sqrt{3^2 \times 7} = 3\sqrt{7}
\]

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

Would you like more details or have any further questions? Here are some related questions you might find helpful:

1. How do you simplify square roots involving larger numbers?
2. What are the steps for finding the prime factorization of a number?
3. How would you approximate \( \sqrt{7} \) to a decimal?
4. How does simplifying square roots help in solving equations?
5. Can all square roots be simplified in a similar manner?

**Tip:** Always check if a number under the square root has a perfect square factor. This helps in simplifying the expression.

Learn how to simplify the square root of 63 through prime factorization, resulting in 3√7. This detailed explanation is perfect for students in Grades 6-8 and covers the core mathematical concepts of square roots and prime factorization.

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