Lesson goal: What kind of numbers will result?

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Suppose $D=a^2+b^2+c^2$, where $a$ and $b$ are consecutive integers and $c=ab$. What type of result do you think $\sqrt{D}$ will be? (From Salkind, 1967.)

A. always an even integer
B. sometimes an odd integer, sometimes not
C. always an odd integer
D. sometimes rational, sometimes not
E. always irrational

Write some code to cycle through 100 or 1000 different numbers and see if you can spot a pattern in the result of $\sqrt{D}$.

Now you try. What do think about $\sqrt{D}$? Choice A, B, C, D, or E?

Type your code here:

See your results here:

The code will not run! Fix $a$ to go from 1 to 100 or 1000, etc. Set up b and c based on the rules stated above. Compute $D$, then $\sqrt{D}$ (use math.sqrt(..)) and see what you get. Dismiss.
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  1. Use [Control]-[C] (Windows) or [⌘]-[C] (MacOS) to copy your code.

  2. Paste it using [Control]-[V] (Windows) or [⌘]-[V] (MacOS) into this page

  3. Then click the "Use on iPhone" button that you'll see.