Squaring a number from 4,901-4,999

mathaholic · 2014-07-12 20:17:24

I was just playing around with a calculator until I found out that 4,913 squared had a property. And so as the other numbers ranging from 4,901 to 4,999. So, here is the trick.

1. Pick a number from 4,901-4,999.
I have here in my hands a number called 4,949.

2. Get the number 24.
So now we have 24,???,???. Question mark means unknown digit.

3. Take the last two digits of the number from step 1.
Here we have 24,49?,???.

4. Subtract the last two digits of the number from step 1 from 100.
Now, we get 100-49, hence 51. But don't add that number yet.

5. Square the result from step 4.
51^2 = 2,601

6. Join the answer from step 3 and step 5. If the answer to step 5 does not have four digits, add more zeroes to the left of the result until you get four digits, then merge steps 3 and 5's result..
Okay, back to the example. So now we have 24,492,601.

7. Calculate the square root of the answer in number 6. If the result is the same from step 1, then congratulations! Show this to your friends.

phrontister · 2014-07-12 23:10:47

Yes, that is cool!

I entered it into Excel, which proved that the formula works for all 4901 to 4999.

I haven't yet worked out what trick causes this to happen, though, nor how or if it works with other ranges.

mathaholic · 2014-07-12 23:13:49

It is because it increments by 9801, 9803 and so on, but the case is that 4900 squared is 24,010,000 which opposes the formula above.

phrontister · 2014-07-13 09:13:00

Ok...thanks. I'll look into that.

mathaholic · 2014-07-24 22:05:10

Are you done yet?

Math Is Fun Forum

#1 2014-07-12 20:17:24

Squaring a number from 4,901-4,999

#2 2014-07-12 23:10:47

Re: Squaring a number from 4,901-4,999

#3 2014-07-12 23:13:49

Re: Squaring a number from 4,901-4,999

#4 2014-07-13 09:13:00

Re: Squaring a number from 4,901-4,999

#5 2014-07-24 22:05:10

Re: Squaring a number from 4,901-4,999

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