I found something interesting(a rule) in Maths...?

Question

And it is:

(1.1).(2.2) = 1.4 = 4 (4=2.2 / we take its square root) = 2
(2.2).(3.3) = 4.9 = 36 (36=6.6) = 6
(3.3).(4.4) = 9.16 = 144 (144=12.12) = 12
(4.4).(5.5) = 16.25 = 400 (400=20.20) = 20
(5.5).(6.6) = 25.36 = 900 (900=30.30) = 30
(6.6).(7.7) = 36.49 = 1764 (1764=42.42) = 42
(7.7).(8.8) = 49.64 = 3136 (3136=56.56) = 56
(8.8).(9.9) = 64.91 = 5184 (5184=72.72) = 72
.....

Be careful about 2 - 6 - 12 - 20 ... 2+4 = 6 , 6 + (4+2) = 12, 12 + (6+2) = 20...Always 2 increases..

Umm..My question is..Did someone find it before?..And in which problems can I use it?

Oh :-)..I don't know age but..I'm under 15..And we hadn't learn it..In which problems can I use it..For example can I use it in number lines ( you know what can you write in stead of the question mark)..

You didn't understand my rule..But ok no problem..Thank u for your answers..

Answer 1

Two things:

As others said, you are doing the square root of x*x*y*y and this is equal to x*y. You would get the same results by doing:
1*2 = 2
2*3 = 6
3*4 = 12
etc.

Now for that other thing you noticed: The sequence 2, 6, 12, 30, 30, 42, 56, 72... The nth term in this sequence is n*(n+1).
n=1 --> 1*2 = 2
n=2 --> 2*3 = 6.
etc.

Now the difference between consecutive terms is going to be:
(n+1)*(n+2) - n*(n+1) = 2n + 2 = 2(n+1) after simplifying. This is why the difference will always increase by 2.

This is nothing new, it is well known that sequences of products behave that way, for example the sequence of squares 1, 4, 9, 16, 25, 36... has the difference between terms increasing by 2 also: 3, 5, 7, 9...

Answer 2

Just trying to understand your "rule"?

Is it that sqrt((x^2)(y^2)) = xy?

i.e. that (x^2)(y^2) = (xy)^2?

If so, sorry to dash your hopes, there's not a big breakthrough here. If I've misunderstood, apologies.

But continue to enjoy playing with numbers!

Answer 3

Well duh

(1.1).(2.2) = (1.2).(1.2) = 2.2 = 4
...
(7.7).(8.8) = (7.8).(7.8) = 56.56 = 3136

You discovered associativity and commutativity for the product.
This could be very useful in calculations and thats probably why it's one of the first things they teach you in school.

Answer 4

It's called number bond's i've just been doing it in maths myself