The given expression is the cube root of 1000, written as:

$\sqrt[3]{1000}$

To solve this:

We know that:

$1000 = 10^3$

Thus, the cube root of $1000$ is:

$\sqrt[3]{10^3} = 10$

So, the value of $\sqrt[3]{1000}$ is $10$.

Would you like more details on cube roots or any further explanation?

Here are 5 related questions you might find interesting:

1. What is the cube root of 27?
2. How do you calculate the cube root of numbers that are not perfect cubes?
3. What is the cube root of 1728?
4. Can you explain the difference between square roots and cube roots?
5. What is the cube root of negative numbers, like $\sqrt[3]{-8}$?

Tip: The cube root of a number $x$ is the value $y$ such that $y^3 = x$. For non-perfect cubes, approximation techniques or calculators are often used.