Question
Which real-world problem is most likely to involve irrational numbers?(1 point)Responsesfinding the total cost of filling up a car's tank based on the price per gallonfinding the total cost of filling up a car's tank based on the price per gallonfinding the side length of a square based on the areafinding the side length of a square based on the areafinding the width of a rectangle based on the area and the lengthfinding the width of a rectangle based on the area and the lengthfinding the diameter of a circle based on the radiusfinding the diameter of a circle based on the radius
Answers
GPT-4o mini
The real-world problem that is most likely to involve irrational numbers is **finding the side length of a square based on the area**.
This is because if you have an area \(A\) of a square and you want to find the side length \(s\), you use the formula \(A = s^2\). Therefore, \(s = \sqrt{A}\). If \(A\) is not a perfect square, then the value of \(s\) will be an irrational number. For example, if \(A = 2\), then \(s = \sqrt{2}\), which is an irrational number.
The other options provided either lead to rational values or would not necessarily yield irrational numbers.
This is because if you have an area \(A\) of a square and you want to find the side length \(s\), you use the formula \(A = s^2\). Therefore, \(s = \sqrt{A}\). If \(A\) is not a perfect square, then the value of \(s\) will be an irrational number. For example, if \(A = 2\), then \(s = \sqrt{2}\), which is an irrational number.
The other options provided either lead to rational values or would not necessarily yield irrational numbers.