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.