Question

$\sqrt3{343} = \square$

Explanation:

Step1: Recall cube of integers

We know that to find the cube root of a number \( n \), we need to find an integer \( x \) such that \( x^3=n \). Let's recall the cubes of small integers.
We know that \( 7\times7\times7 = 7^3\). Calculating \( 7\times7 = 49 \), then \( 49\times7=343 \). So \( 7^3 = 343 \).

Step2: Apply cube - root definition

By the definition of cube root, if \( x^3 = a \), then \( \sqrt[3]{a}=x \). Since \( 7^3 = 343 \), then \( \sqrt[3]{343}=7 \).

Answer:

\( 7 \)