To solve \((12 \sqrt{2})^2\), follow these steps:

1. Start by squaring the entire expression:

\[
(12 \sqrt{2})^2 = 12^2 \times (\sqrt{2})^2
\]

2. Calculate the square of 12:

\[
12^2 = 144
\]

3. Now, calculate the square of \(\sqrt{2}\):

\[
(\sqrt{2})^2 = 2
\]

4. Finally, multiply the results:

\[
144 \times 2 = 288
\]

So, \((12 \sqrt{2})^2 = 288\).

Would you like further details or have any questions? 

Here are some related questions:
1. What is the square of \(15 \sqrt{3}\)?
2. How do you simplify \(8 \sqrt{5} \times 2 \sqrt{5}\)?
3. What is the result of \(\sqrt{50} \times \sqrt{2}\)?
4. How do you square a binomial like \((3 + \sqrt{5})^2\)?
5. What is the value of \((\sqrt{7})^4\)?

**Tip:** When squaring a square root, remember that the square and the square root cancel each other out, simplifying the expression.

Learn how to solve the expression (12 square root of 2)^2 with a detailed step-by-step solution. This problem involves key mathematical concepts such as exponents and square roots. Suitable for students in Grades 6-8.

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