Squaring of numbers near a power of ten

[krazedkat]

for instance:
near 10
near 100
near 1000
near 10000
near 100000
near 1000000
near 10000000
and so forth

It is fairly simple.

For instance:

18^2 first take 18 and subtract 10 (the number it's near), this will give you 8.
now add the number you got to the number you are squaring, in this case 18+8=26.
After this square the first number you got, in this case 8, and tack it on to the last spot (after the 6).
8^2 = 64
26+064=
26
064
----
324 <---- tada, you're done.

This can be applied to any other similar instance:

107^2
114
7^2 = 49
114
00049
------
11449 <- that's the right answer

1007^2
1014
0000049
--------
1014049 <- done

Now you notice that we go up by odd numbers for the nulls that we put in. For 10 you put in one null, 100 is 3, 1000 is 5, 10000 is 7 and so forth. Enjoy this pattern, I simply love it!

 

[Karma_mybb_import2519]

Your wish has been granted.

 

[krazedkat]

Please don't spam though man, do you have anything to say about my pattern?

 

[ttomthebomb]

I actually understand this, I love the pattern, simple enough to follow.

 

[krazedkat]

Thank you very much . I just looked around and it seems others have found this out before too.

btw: top poster is me , and I have 10.5% of this forums' posts .

 

[ttomthebomb]

20^2 = 40
20 + 040

20
040
_____
240

Simple enough.

 

[krazedkat]

Wrong, it'd be:

20+10=30
then
10^2=100
100
30
----
400

That's why this pattern is only for numbers starting in 1 I believe.

 

[ttomthebomb]

Oh, okay, I was under the impression that is was generic.

 

[krazedkat]

I don't think so... Unless I am direly missing something :\.

 

[Adam_mybb_import1422]

Cool you found a pattern, but why does it work?

 

[krazedkat]

Yes, I demonstrated that it did, didn't I?

 

[Adam_mybb_import1422]

Yes, I demonstrated that it did, didn't I?

I suppose I didn't see it then. I've never been the best at math.

 

[krazedkat]

It's okay man, I just mentally destroy you in the subject of maths, that's all .

 

[Adam_mybb_import1422]

It's okay man, I just mentally destroy you in the subject of maths, that's all .

Maybe someday we'll put that to the test

btw, grats on 200 man.

 

[Adam_mybb_import1422]

That's why this pattern is only for numbers starting in 1 I believe.

I've figured out why it only works with 1 in the 10s (or 100s, ect.) place.

[(10t+u)+u]10+u^2=(10t+u)^2
=
[10t+2u]10+u^2=100t^2+20tu+u^2
=
100t+20u+u^2=100t^2+20tu+u^2

t= digit in 10s place (1)
u= digit in 1s place (8)

100+160+64=100+160+64

See what I'm saying? Did I do it right?

 

[krazedkat]

I think you did ^^. Nice work . Thanks by the way.

 

[Adam_mybb_import1422]

I think you did ^^. Nice work . Thanks by the way.

Sweet, I think I'll play around with that equation a little more +rep for the great thread.

 

[maplman]

I saw this in a math tricks book.

 

[krazedkat]

Really? Can you link me please . Is it the exact same or is it slightly different? Because I've seen patterns similar in such books but not this one per say.

 

[Rhythm_mybb_import2559]

Pretty interesting pattern you've found there. Not practical, but cool nonetheless.