Which real-world problem is

Question

most likely to involve irrational
numbers?
finding the diameter of
a circle based on the
radius
finding the width of a
rectangle based on the
area and the length
finding the side length
of a square based on
the area
finding the total cost of
filling up a car’s tank
based on the price per
gallon

Answer 1

The real-world problem most likely to involve irrational numbers is:

Finding the diameter of a circle based on the radius.

This is because the relationship between the diameter (d) and the radius (r) of a circle is given by the formula \( d = 2r \). However, when dealing with circles, often the use of the radius also relates to calculations involving π (pi), which is an irrational number. For instance, if you need to calculate the circumference or area of the circle using the radius, you would also be working with π, leading to irrational results.

In contrast, the other scenarios (finding the width of a rectangle from area and length, side length of a square from area, and calculating total cost) do not necessarily involve irrational numbers, as they can often be computed with rational numbers.