Question

$\sqrt3{512} = \square$

Explanation:

Step1: Recall cube of integers

We know that to find the cube root of a number, we need to find an integer \( x \) such that \( x^3=x\times x\times x \) equals the number inside the cube root. Let's recall the cubes of some integers. For example, \( 8\times8\times8 = 512 \), because \( 8\times8 = 64 \) and \( 64\times8=512 \).

Step2: Apply cube root definition

The cube root of a number \( a \), denoted as \( \sqrt[3]{a} \), is a number \( x \) such that \( x^3=a \). Since \( 8^3 = 512 \), by the definition of cube root, \( \sqrt[3]{512}=8 \).

Answer:

\( 8 \)