To solve the equation [tex]\( n^3 = 8 \)[/tex] for [tex]\( n \)[/tex], follow these steps:
1. Understand the problem: The equation [tex]\( n^3 = 8 \)[/tex] asks us to find the value of [tex]\( n \)[/tex] such that when [tex]\( n \)[/tex] is cubed, the result is 8.
2. Isolate the variable: To solve for [tex]\( n \)[/tex], we need to undo the operation of cubing. The inverse of cubing a number is taking the cube root.
3. Take the cube root of both sides: To isolate [tex]\( n \)[/tex], take the cube root of both sides of the equation:
[tex]\[
n = \sqrt[3]{8}
\][/tex]
4. Compute the cube root: Determine the cube root of 8. Since [tex]\( 2 \times 2 \times 2 = 8 \)[/tex], we find that:
[tex]\[
n = 2
\][/tex]
Thus, the solution to the equation [tex]\( n^3 = 8 \)[/tex] is [tex]\( n = 2 \)[/tex].
