{"id":169215,"date":"2024-11-19T06:02:59","date_gmt":"2024-11-19T06:02:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=169215"},"modified":"2024-11-19T06:03:01","modified_gmt":"2024-11-19T06:03:01","slug":"a-square-rug-has-an-area-94-ft","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/a-square-rug-has-an-area-94-ft\/","title":{"rendered":"A square rug has an area 94 ft."},"content":{"rendered":"\n

A square rug has an area 94 ft. Write the side length as a square root. Then decide if the side length is a rational number.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine the side length of the square rug, we need to use the formula for the area of a square, which is:<\/p>\n\n\n\n

[
\\text{Area} = s^2
]<\/p>\n\n\n\n

where ( s ) represents the side length of the square. Given that the area of the square rug is 94 square feet, we can set up the equation:<\/p>\n\n\n\n

[
s^2 = 94
]<\/p>\n\n\n\n

To solve for ( s ), we take the square root of both sides of the equation:<\/p>\n\n\n\n

[
s = \\sqrt{94}
]<\/p>\n\n\n\n

So, the side length of the rug is ( \\sqrt{94} ) feet.<\/p>\n\n\n\n

Is ( \\sqrt{94} ) a rational number?<\/h3>\n\n\n\n

A rational number is a number that can be expressed as the quotient of two integers (i.e., as ( \\frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \\neq 0 )). A number is irrational if it cannot be expressed as a simple fraction and its decimal form goes on forever without repeating.<\/p>\n\n\n\n

To check if ( \\sqrt{94} ) is rational, we need to determine whether 94 is a perfect square. A perfect square is a number whose square root is an integer. In the case of 94, we see that:<\/p>\n\n\n\n