If the diagonal of the cube is 3 units, then the edge of the cube is.

Let us denote the diagonal of the cube BC and consider the right-angled triangle ABC

Let AB = x unit.

Using the Pythagorean theorem for right-angled triangles, we compose the equation:

AB ^ 2 + AC ^ 2 = BC ^ 2 (*)

Find the length of the AC

To do this, consider a right-angled triangle ADC

Because all edges of a cube are equal, then AD = AC = AB = x units.

By the Pythagorean theorem

AD ^ 2 + DC ^ 2 = AC ^ 2

or

x ^ 2 + x ^ 2 = AC ^ 2

We get

AC ^ 2 = 2x ^ 2

Substituting the value AC ^ 2 into (*), we get

x ^ 2 + 2x ^ 2 = 3 ^ 2

3x ^ 2 = 9

x ^ 2 = 3

x = √3

Answer: √3 units.