Question

a square rug has an area 100 ft². write the side length as a square root. then decide if the side length is a rational number.
the rug has side length \\(sqrt{100}\\) ft.
is the side length a rational number?
○ no
○ yes

Explanation:

Step1: Recall area of square formula

The area \( A \) of a square with side length \( s \) is given by \( A = s^2 \). We know \( A = 100 \, \text{ft}^2 \), so we solve for \( s \): \( s=\sqrt{A} \).

Step2: Calculate the square root

Substitute \( A = 100 \) into the formula: \( s = \sqrt{100} \). We know that \( 10^2 = 100 \), so \( \sqrt{100}=10 \).

Step3: Determine if 10 is rational

A rational number is a number that can be expressed as \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q
eq0 \). \( 10=\frac{10}{1} \), so it is rational.

Answer:

The side length as a square root is \( \sqrt{100} \) ft (which simplifies to 10 ft), and the side length is a rational number (Yes).