1. ## also

my teacher wants us to convince her that 121 is a square number no matter in what base it is written. how do i do that?

2. Hello, t-lee!

My teacher wants us to convince her that 121 is a square number
no matter in what base it is written.

The number $121_b$ means: . $1\!\cdot\!b^2 + 2\!\cdot\!b + 1$

And we see that: . $b^2 + 2b + 1 \:=\:(b+1)^2$ . . . a square number.

Will that satisfy your teacher?

3. Originally Posted by Soroban
Hello, t-lee!

The number $121_b$ means: . $1\!\cdot\!b^2 + 2\!\cdot\!b + 1$

And we see that: . $b^2 + 2b + 1 \:=\b+1)^2" alt="b^2 + 2b + 1 \:=\b+1)^2" /> . . . a square number.

Will that satisfy your teacher?

Or you could do it by demonstration: $11_b^2 = 121_b$ in all bases since 1 + 1 = 2 in all bases. (Except, of course, binary!)

-Dan

4. Those both are great answers, but how do I explain that in sentence form to her? She also wants me to explain it that way. Explaining why and how. If you could help me with this I would be greatly appreciative of you.

thanks,
t-lee