https://file.aiquickdraw.com/mathbot/file/17254739139470nnh1q0a.jpg

The expression shown in the image is \((\sqrt{2})^3\).

To solve this:

1. Recognize that \((\sqrt{2})^3\) means "the cube of the square root of 2."
2. Calculate the cube of \(\sqrt{2}\):

\[
(\sqrt{2})^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2}) 
\]

Since \(\sqrt{2} \times \sqrt{2} = 2\), this simplifies to:

\[
2 \times \sqrt{2} = 2\sqrt{2}
\]

Thus, \((\sqrt{2})^3 = 2\sqrt{2}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify the expression \((\sqrt{a})^3\) for any positive number \(a\)?
2. What is the value of \(\sqrt{2}\) approximately?
3. How would the result change if the expression was \((\sqrt{3})^3\) instead?
4. What are the properties of exponents when applied to square roots?
5. How can you express \((\sqrt{2})^n\) in a more general form for any integer \(n\)?

**Tip:** When raising square roots to a power, remember that \((\sqrt{a})^2 = a\). This helps simplify many expressions involving roots and exponents.

Understand how to simplify the expression (√2)^3 through a clear and detailed step-by-step solution. This problem involves key concepts in exponentiation and square roots, making it suitable for students in Grades 8-10.

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