Question

$\sqrt3{729} = \square$

Explanation:

Step1: Recall cube of numbers

We know that to find the cube root of a number, we need to find a number \( x \) such that \( x^3=x\times x\times x \) equals the number inside the cube root. Let's recall the cubes of some integers.
We know that \( 9\times9\times9 = 9^3\). Calculating \( 9\times9 = 81 \), then \( 81\times9=729 \).

Step2: Apply cube root definition

The cube root of a number \( a \), denoted as \( \sqrt[3]{a} \), is the number \( x \) such that \( x^3 = a \). Since \( 9^3=729 \), by the definition of cube root, \( \sqrt[3]{729}=9 \).

Answer:

\( 9 \)