Question

which value of n makes the following equation true?
$sqrt3{n}=8$
2
16
24
512

Explanation:

Step1: Recall the definition of cube root

The cube root of a number \( n \), denoted as \( \sqrt[3]{n} \), is a value \( x \) such that \( x^3 = n \). So if \( \sqrt[3]{n}=8 \), then we need to find \( n \) such that when we take the cube of 8, we get \( n \).

Step2: Calculate \( 8^3 \)

We know that \( 8^3=8\times8\times8 \). First, \( 8\times8 = 64 \), then \( 64\times8=512 \). So \( n = 512 \) because \( \sqrt[3]{512}=8 \) (since \( 8^3 = 512 \)).

Answer:

512