Does Squaring Any Number Follow a Specific Pattern?

[DaveDem]

In math class my teacher said that if you take any base or A and square it that the answer is howmany times two goes into the base multiplied by the base times 2, does this always work?

 

[jedishrfu]

Can you give a couple of examples in different bases?

 

[DaveDem]

16 squared
16/2=8 16*2=32
32*8=256

 

[DaveDem]

500 squared
500/2=250 500*2=1000
250*1000=250000

 

[DaveDem]

13 squared
13/2=6.5 13*2=26
6.5*26=169

 

[jedishrfu]

Have you tried it with other nunbers like 3, 5 or 7?

7x7=49

7/2=3.5

7*2=14

3.5 x 14 = 49

Like that?

 

[jedishrfu]

Okay so basically you are dividing by two and then multiplying by two so the operations cancel out right?

 

[DaveDem]

yes exactly! i kinda came up with it but said it was my math teacher cause of the whole "if it doesn't come from someone with proof of knowledge we don't want to hear it" thing

 

[jedishrfu]

Okay so you understand how it works now?

 

[jedishrfu]

Many of these math tricks work in a similar way by trying to hide the fact that you are multiplying by a factor early and then cancelling it out by dividing later on using valid math operations throughout the process.

 

[jedishrfu]

For example in your case you could say to add the number to itself instead of using times two to hide that fact and people may be fooled at first.

 

[jedishrfu]

Its like that famous rhyme: As I was going to St Ive's I met a man with seven wives and each wife had seven ...

And then you are asked how many were going to St Ives:

http://en.m.wikipedia.org/wiki/As_I_was_going_to_St_Ives

 

[jedishrfu]

Theres no need to preface questions with my math teacher said unless they really said it. Its best to be honest rather than impune the integrity of your teacher for the sake of an answer.