Digit Multiplication Time!

Algebra Level 2

Let $A$ be a positive single-digit number, such that:

What is $\overline{AAA}^2$ ?

Note: The leading digits for both $A^2$ and $\overline{AA}^2$ are nonzero.

1 solution

Zach Abueg
May 20, 2017

Given that $A > 0$ and $(A)^2$ is a single-digit number, we know that $1 \leq A \leq 3$ .

Given that $(AA)^2$ is a four-digit number, we know $A \neq 1$ , so we are left with $A = 2$ or $A = 3$ .

$22^2 = 484 \\ 33^2 = 1089$

$A = 3 \Longrightarrow (AAA)^2 = 333^2 = \boxed{110889}$