Square of 1 Less than Number Base/Examples/5

Example of Square of 1 Less than Number Base

The square of $5$ is expressed in base $6$ as:

$5^2 = \left[{41}\right]_6$

Proof

In base $10$:

\(\ds 5^2\)

\(=\)

\(\ds \left({6 - 1}\right)^2\)

\(\ds \)

\(=\)

\(\ds 6^2 - 2 \times 6 + 1\)

\(\ds \)

\(=\)

\(\ds 4 \times 6 + 1\)

Hence the result.

$\blacksquare$