Question

the area of a square can be represented by the expression $x^{10}$. which monomial represents a side of the square?
$\bigcirc\\ x^2$
$\bigcirc\\ x^5$
$\bigcirc\\ x^{20}$
$\bigcirc\\ x^{100}$

Explanation:

Step1: Recall area of square formula

The area \( A \) of a square with side length \( s \) is given by \( A = s^2 \). So, to find the side length, we need to take the square root of the area.

Step2: Apply square root to the area expression

Given the area is \( x^{10} \), we find the side length \( s \) by calculating \( s=\sqrt{x^{10}} \). Using the exponent rule \( \sqrt{a^m}=a^{\frac{m}{2}} \), we have \( s = x^{\frac{10}{2}}=x^5 \).

Answer:

B. \( x^5 \) (assuming the second option is labeled B, with the option text \( x^5 \))