Why does a square equals a second power?

Answer 1

The "square" of a number is named after the shape. Since the area of any rectangle is calculated by multiplying its width by its length, and a square has the same width as length, its area is calculated by multiplying that number by itself.

A = L x W

L = W ∴ A = L x L ∴ A = L2

Similarly, since a cube has equal length, width, and height, the volume of the cube is calculated in a similar manner, so a number to the third power is said to be "cubed."

V = L x W x H

L = W = H ∴ V = L x L x L ∴ V = L3