Question

The area of a square is 64 n Superscript 36square units. What is the side length of one side of the square?
A. 8 n Superscript 6 units
B. 8 n Superscript 18 units
C. 64 n Superscript 6 units
D. 64 n Superscript 18 units

Answer 1

To find the side length of a square given its area, we can use the formula for the area of a square:

\[
\text{Area} = (\text{side length})^2
\]

Given that the area of the square is \( 64n^{36} \) square units, we can set up the equation:

\[
(\text{side length})^2 = 64n^{36}
\]

To find the side length, we take the square root of both sides:

\[
\text{side length} = \sqrt{64n^{36}}
\]

Calculating the square root of each part:

1. The square root of \( 64 \) is \( 8 \).
2. The square root of \( n^{36} \) is \( n^{36/2} = n^{18} \).

Thus, the side length is:

\[
\text{side length} = 8n^{18} \text{ units}
\]

Looking at the options provided, we see that this matches option:

**B. \( 8n^{18} \) units.**