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Challenge Answer 170

The square that starts at 999

You only need to do four tests to get the answer to this question.

Since the number square must start with 999, let's test numbers 9990, 99900, 999000, and 9990000 to see what their roots are.

If you look at the first three results, you will see that the natural number following the root number will not produce the result we want. For example, in the first case, where the root was 99.9499…, if we take the next natural (100), we get 1002= 10,000 (doesn't fit us).

Now if you test the last result, where we find the root 3160,6961…, the next natural number would be 3161. Let's see if it suits us:

31612 = 9991921

Question solved! The number we are looking for is 3161.

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