Cube has an edge length of A, which, which measurement will require use of irrational numbers

Answer 1

In mathematics, the only aspect of a cube that would require the use of irrational numbers is when calculating the length of its space diagonal.

A cube with an edge length \( A \) has the following properties:

1. Volume: The volume of the cube is given by \( V = A^3 \).
2. Surface Area: The surface area of the cube is given by \( SA = 6A^2 \).
3. Space Diagonal: The length of the space diagonal \( d \) (the diagonal running from one corner of the cube to the opposite corner) can be calculated using the formula: \[ d = A \sqrt{3} \]

Here, \( \sqrt{3} \) is an irrational number (approximately 1.732). Therefore, to find the length of the space diagonal of the cube, you would need to use an irrational number.

Calculating the volume and surface area, on the other hand, can be done using rational numbers if \( A \) itself is a rational number.