To solve the square root of 567 and rationalize it, we can first simplify the radical expression:

1. Factor 567:
   $567 = 3^4 \times 7$

2. Now simplify the square root:
   $\sqrt{567} = \sqrt{3^4 \times 7}$

   Since $3^4$ is a perfect square, we can take the square root of $3^4$, which is $3^2 = 9$.

   Thus,
   $\sqrt{567} = 9\sqrt{7}$

There is no need to further rationalize this expression, as it is already simplified in its simplest form. The square root of 567 simplifies to:

$\sqrt{567} = 9\sqrt{7}$

Let me know if you need more details on this process!

Here are 5 related questions for you to explore further:

1. How would you simplify $\sqrt{648}$?
2. What is the square root of a perfect square number like 576?
3. How can you approximate the value of $\sqrt{567}$ without simplifying it?
4. How would you rationalize a denominator like $\frac{1}{\sqrt{7}}$?
5. What is the difference between simplifying and rationalizing a square root?

Tip: Always look for the largest perfect square factor to simplify square roots efficiently!