To find the side length of the square given that its area is [tex]\(64 n^{36}\)[/tex] square units, let's follow these steps:
1. Recall the formula for the area of a square: The area [tex]\(A\)[/tex] of a square is given by [tex]\(A = \text{side length}^2\)[/tex].
2. Express the given area in terms of the side length: Here, the area is given as [tex]\(64 n^{36}\)[/tex] square units. So, we can write:
[tex]\[
\text{side length}^2 = 64 n^{36}
\][/tex]
3. Find the side length: To find the side length, we need to take the square root of both sides of the equation:
[tex]\[
\text{side length} = \sqrt{64 n^{36}}
\][/tex]
4. Simplify the square root:
- The square root of [tex]\(64\)[/tex] is [tex]\(8\)[/tex], since [tex]\(8^2 = 64\)[/tex].
- The square root of [tex]\(n^{36}\)[/tex] is [tex]\(n^{18}\)[/tex], since [tex]\((n^{18})^2 = n^{36}\)[/tex].
Thus,
[tex]\[
\text{side length} = 8 n^{18}
\][/tex]
Therefore, the side length of one side of the square is [tex]\(8 n^{18}\)[/tex] units. The correct choice is:
[tex]\[ 8 n^{18} \text{ units} \][/tex]
