find the value of \\(\\sqrt3{1000}\\).

Explanation:

Step1: Recall cube root definition

The cube root of a number ( x ), denoted as ( \sqrt[3]{x} ), is a number ( y ) such that ( y^3 = x ). So we need to find ( y ) where ( y^3 = 1000 ).

Step2: Find the number whose cube is 1000

We know that ( 10\times10\times10 = 10^3 = 1000 ). So by the definition of cube root, ( \sqrt[3]{1000}=10 ).

Answer:

( 10 )