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

Answer 1

The measurement of the diagonal of a cube will require the use of irrational numbers.

To find the diagonal, we can use the Pythagorean theorem. The diagonal, D, is equal to the square root of the sum of the squares of two adjacent edges. For a cube with an edge length of a, the diagonal can be calculated as follows:

D = √(a^2 + a^2 + a^2) = √(3a^2) = a√3

Since the edge length a is rational, the diagonal a√3 will be irrational, as it involves the square root of 3 which is an irrational number.