A cube has an edge length, a

, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.

1 answer

In a cube with an edge length \( a \), all of its edges are of equal length \( a \). The volume \( V \) of the cube is calculated using the formula:

\[ V = a^3 \]

Since \( a \) is a rational number, \( a^3 \) is also a rational number.

However, when you calculate the space diagonal \( d \) of the cube, you use the formula:

\[ d = a\sqrt{3} \]

In this case, since \( a \) is a rational number, \( \sqrt{3} \) is an irrational number. Therefore, the measurement that will require the use of irrational numbers is the space diagonal of the cube, \( d \).