To solve the expression \( \left(3\sqrt{8}\right)^2 \), let's break it down step by step:

1. First, simplify \( \sqrt{8} \). 
   \[
   \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
   \]
   
2. Now substitute \( \sqrt{8} \) with \( 2\sqrt{2} \):
   \[
   \left(3\sqrt{8}\right)^2 = \left(3 \times 2\sqrt{2}\right)^2
   \]
   Simplify inside the parentheses:
   \[
   = \left(6\sqrt{2}\right)^2
   \]

3. Now square both parts of the expression:
   \[
   = 6^2 \times \left(\sqrt{2}\right)^2 = 36 \times 2 = 72
   \]

Thus, the value of \( \left(3\sqrt{8}\right)^2 \) is \( 72 \).

Would you like more details on any of the steps or concepts? 

Here are 5 related questions to expand your understanding:
1. How do you simplify square roots of non-perfect squares like \( \sqrt{50} \)?
2. What happens when you raise a square root to a fractional exponent?
3. Can you apply this process to cube roots as well?
4. How do you handle exponents when they apply to complex expressions?
5. What is the general rule for multiplying and squaring radical expressions?

**Tip:** When simplifying square roots, always look for perfect square factors!

Learn how to simplify and square the radical expression (3√8)². This step-by-step guide covers key concepts like simplifying square roots and applying exponent rules, making it ideal for students in Grades 8-10.

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