Hey there!
The answer to your question is one zero.
To solve this, we can first start by finding the cube root.
[tex]\sqrt[3]{1000}[/tex]
The answer to this is [tex]10[/tex], because [tex]10 * 10 * 10 = 1000[/tex]
Now, we can see that there is one zero at the end of [tex]10[/tex].
Hope it helps and have a great day/night! Stay safe!