Answer:
Hence, the exact side length of the rug is s = √(42) ft.
Explanation:
To find the exact side length of the square rug, we can use the formula for the area of a square. The formula for the area of a square is given by A = s^2, where A represents the area and s represents the side length of the square.
In this case, we are given that the area of the square rug is 42ft^2. So, we can set up the equation as follows:
42ft^2 = s^2
To solve for s, we need to take the square root of both sides of the equation:
√(42ft^2) = √(s^2)
Simplifying further:
√(42ft^2) = s
Taking the square root of 42ft^2 gives us an irrational number, which means it cannot be expressed as a simple fraction or decimal. Therefore, we can only provide an exact answer in terms of a radical.
The square root of 42 can be simplified as √(42) = √(2 * 3 * 7) = √(2) * √(3) * √(7).