To solve the equation [tex]\( n^3 = 60 \)[/tex] for [tex]\( n \)[/tex], you need to follow these steps:
1. Identify the equation: The given equation is [tex]\( n^3 = 60 \)[/tex].
2. Isolate [tex]\( n \)[/tex]: To solve for [tex]\( n \)[/tex], you need to undo the cube operation. The inverse operation of cubing a number is taking the cube root.
3. Take the cube root: Apply the cube root to both sides of the equation to isolate [tex]\( n \)[/tex]:
[tex]\[
n = \sqrt[3]{60}
\][/tex]
4. Choose the correct option: Among the given options, you need to identify which one matches [tex]\( n = \sqrt[3]{60} \)[/tex].
The options provided are:
A. [tex]\( n = \sqrt[3]{60} \)[/tex] (cube root of 60)
B. [tex]\( n = \sqrt{60} \)[/tex] (square root of 60)
C. [tex]\( n = 20 \)[/tex]
D. [tex]\( n = 180 \)[/tex]
Comparing these options, it is clear that the correct option representing the solution is:
Option A: [tex]\( n = \sqrt[3]{60} \)[/tex]
Therefore, the answer is A.
