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.