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  1. #1
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    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?
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  2. #2
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    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 $\displaystyle 121_b$ means: .$\displaystyle 1\!\cdot\!b^2 + 2\!\cdot\!b + 1$

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

    Will that satisfy your teacher?

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, t-lee!


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

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

    Will that satisfy your teacher?

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

    -Dan
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  4. #4
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    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
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