https://file.aiquickdraw.com/mathbot/file/17297729379530dktircu.jpg

From the image, we see that a factor tree is shown for the number 1,764. The factorization of 1,764 is as follows:

1,764  
↓  
2 × 882  
↓  
2 × 441  
↓  
3 × 3 × 49  
↓  
7 × 7

Thus, the prime factorization of 1,764 is \( 2^2 \times 3^2 \times 7^2 \).

The task is to simplify \( \sqrt{1,764} \).

Since \( 1,764 = 2^2 \times 3^2 \times 7^2 \), we can take the square root by simplifying each factor:

\[
\sqrt{1,764} = \sqrt{2^2 \times 3^2 \times 7^2} = 2 \times 3 \times 7 = 42.
\]

Thus, the simplest form of \( \sqrt{1,764} \) is 42, and the correct answer should be "42."

It seems that the factorization \( 2^2 \times (3^2) \times (7^2) \) is shown in the blue selected option, but the final simplified form is 42.

Would you like more details or have any questions?

Here are some relative questions:
1. What is the prime factorization of a given number?
2. How do you simplify square roots of perfect squares?
3. Why do factors need to be prime in a factor tree?
4. Can every number be expressed as a product of prime numbers?
5. What are the rules for simplifying expressions involving square roots?

**Tip**: Always ensure all prime factors are raised to the correct power before taking roots or simplifying.

Learn how to simplify the square root of 1,764 by using its prime factorization. This problem demonstrates how to break down a number into prime factors and simplify the square root using properties of exponents. Suitable for students in Grades 6-8.

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