https://file.aiquickdraw.com/mathbot/file/1726227344633hg0ic1p2.jpg

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!

How do you simplify the square root of 567?

Learn how to simplify the square root of 567 step by step. This problem involves using the prime factorization method to simplify radicals, resulting in the expression 9√7. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation