The expression in the image asks for the cube root of 64, denoted by $\sqrt[3]{64}$.

Solution:

The cube root of a number $x$, $\sqrt[3]{x}$, is a number $y$ such that: $y^3 = x$

For $x = 64$: $y^3 = 64$

We know: $4^3 = 4 \times 4 \times 4 = 64$

Thus: $\sqrt[3]{64} = 4$

Final Answer:

$\boxed{4}$

Would you like a detailed explanation or help with related concepts?

Here are 5 questions to consider:

1. What is the cube root of other perfect cubes like $\sqrt[3]{27}$ or $\sqrt[3]{125}$?
2. How does the cube root differ from the square root mathematically?
3. How can cube roots be approximated for non-perfect cubes like $\sqrt[3]{50}$?
4. What is the general formula for solving $\sqrt[3]{x} = y$?
5. How are cube roots represented in different contexts, such as physics or engineering?

Tip:

To quickly determine cube roots of perfect cubes, memorize the cubes of integers up to 10 (e.g., $1^3, 2^3, 3^3, \dots, 10^3$).