I am currently attending a conference that is housing everybody in a rather large hotel. When I checked in last night I was given room 3025.

My first thought when I looked at the number was “Ah, this is a perfect square”. So as I carried my bags to the room, I mentally set about working out the square root of my room number.

Being lazy, I did this the easiest way I could think of: I multiplied by four to find a number with zeros at the end. This gave me 12100. Which is clearly 121 × 100, or 112 × 102, or 1102.

Having multiplied by four to get the square of 110, I now needed to divide 110 by two. So by the time I arrived at my room, I knew that the square root of 3025 is 55.

But how did I know, in that first moment at the registration desk, that 3025 is a perfect square?

I remember that I had immediately been struck by seeing “30” followed by “25”. This suggests that I may have subconsciously recognized the visual pattern 2500 + 500 + 25 as an instance of (a2)100 + (2a)10 + a2, or (10a + a)2.

If this is true, it would mean that my conscious and subconscious minds had gone in completely different directions. And it would also mean that my subconscious mind had been a whole lot quicker than my conscious mind.

Alas, if only my conscious mind could be as quick as my subconscious mind.

One Response to “3025”

  1. Zhuoheng says:

    Here is an interesting method to calculate the square of 10n+5. Write down the result of n(n+1), then append 25 to the right side of it. Actually I mean (10n+5)^2 = n(n+1)*100 + 25. Now you must be able to tell the square root of anything like this, such as 3025, 4225, and 7225.

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