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#1 2014-02-11 13:07:26

TheTick
Member
Registered: 2012-12-03
Posts: 27

Something I noticed with square roots.

So first off I have not posted here for a LONG time, ever since I switched my major to nursing I have been quite busy and exposed to and needing to do much less maths than before(previous major was architecture.)

I still like it, however finding time is harder.

So back on topic, I was playing around in excel and happened to notice a peculiar thing with square roots.. maybe not particularly useful or exciting, but neat.

Here is what I found,

If you start with your first perfect square root 1 it takes 1 number to get there(from 0)

Next perfect square root, 4, will take 3 numbers to get to from the last perfect square root(1+3=4)

Next perfect square root, 9, will take 5 numbers to get to from the last perfect square root(4+5=9)

see the pattern yet?

to find the perfect square roots you just need to be able to add and understand odd numbers..

1=1
1+3=4
1+3+5=9
1+3+5+7=16
1+3+5+7+9=25
1+3+5+7+9+11=36


Just thought that was kind of neat, so I decided to share.. though lots of people on this forum probably already knew this =P.

Last edited by TheTick (2014-02-11 13:09:51)


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#2 2014-02-11 14:15:16

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,937
Website

Re: Something I noticed with square roots.

Welcome back!

The right term is perfect square

Theorem The sum of first n odd numbers is n[sup]2[/sup]

Proof The first n odd numbers form an arithmetic progression starting from 1, with common difference 2 and n terms.

Thus, the sum of the numbers is


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#3 2014-02-11 21:15:56

bob bundy
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Registered: 2010-06-20
Posts: 7,182

Re: Something I noticed with square roots.

And here in pictures.

Just thought that was kind of neat, so I decided to share.. though lots of people on this forum probably already knew this .

But you made an original (for you) discovery and that's great!  smile

Bob

View Image: thetick.gif

Last edited by bob bundy (2014-02-11 21:18:06)


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#4 2014-02-12 01:16:53

Nehushtan
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Registered: 2013-03-09
Posts: 630
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Re: Something I noticed with square roots.

In other words …


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