15. write the side length of the square rug as a square root. is the side length a rational or irrational…

Explanation:

Step1: Recall area formula for square

The area formula of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 100$ square feet, we solve for $s$. [s^{2}=100]

Step2: Solve for side - length

Taking the square root of both sides, we get $s=\sqrt{100}$. Since $10\times10 = 100$ and $(- 10)\times(-10)=100$, but the side - length of a rug cannot be negative, so $s = \sqrt{100}=10$ feet.

Step3: Determine if the number is rational or irrational

A rational number is a number that can be written as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q\neq0$. Since $10=\frac{10}{1}$, it is a rational number.

Answer:

The side - length of the square rug written as a square root is $\sqrt{100}$ feet. The side - length is a rational number because $\sqrt{100}=10$, and 10 can be written as $\frac{10}{1}$, which is in the form of a fraction $\frac{p}{q}$ with $p = 10$ and $q = 1$ (where $p,q$ are integers and $q\neq0$).