A cube has an edge length, a , that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.

Question

(1 point)
Responses

the surface area of the cube
the surface area of the cube

the area of one of the cube’s faces
the area of one of the cube’s faces

the diagonal of one of the cube’s faces
the diagonal of one of the cube’s faces

the volume of the cube

Answer 1

The measurement that will require the use of irrational numbers is:

the diagonal of one of the cube’s faces.

To find the diagonal \( d \) of a face of the cube, you would use the formula:

\[ d = a\sqrt{2} \]

where \( a \) is the edge length of the cube. Since the edge length \( a \) is rational, \( \sqrt{2} \) is an irrational number, making \( d \) an irrational measurement.