Cool & Useless Math Trick

[Sayu]

We can actually find the square of a number using the number before.
Let's say we are trying to find the square of 3, well if we know the square of the number before it, 2, we can get the answer by squaring the number before, adding the number pre-squaring, twice and adding 1.

3² = 9
2² = 4
4 + 2 + 2 + 1 = 9

This happens because we have 2 sets of 2's, by adding an extra 2 we now have 3 sets of 2's. The second 2 falls into the first 2 sets of 2's making it 2 sets of 3's. The one goes into the third 2 making it 3 sets of 3's.

This works on basically any square numbers

21² = 20² + 20 + 20 + 1
441

 

[SailusGebel]

 

[Zirrboy]

This works with any pair of numbers, they don't have to be positive, or even whole.
(a + b)² = (a + b)*(a + b) = a² + 2ab + b²

 

[Otjag]

Ahh yes the binomial formula, the horror of 6th grade

 

[NotaNuffian]

Quadratic equation...

Useful-ish when you try to square a number

 

[LilRora]

That's not really useless imo. It can really help if you don't remeber a large square number, like 41². You can use this to quickly calculate in your mind.

If you combine it with that:

(a + b)² = (a + b)*(a + b) = a² + 2ab + b²

and a bit of practice, you can calculate almost any square number in your mind with ease, provided it's reasonably small. Two digits for starters.

Edit: You can use it to find any number including 1 (1² = 0² + 0 + 0 + 1), though it can get confusing if you go into negatives.

 

[Jemini]

This works with any pair of numbers, they don't have to be positive, or even whole.
(a + b)² = (a + b)*(a + b) = a² + 2ab + b²

Ahh, right, huh. So that's how the trick at the start works.
3 squared = (2 + 1) squared.
Or, to put this in variable terms, if we let a = X - 1, then X^2 = (a + 1)^2.

That's how this one works.

(Also, how do you do exponents?)

 

[Zirrboy]

(Also, how do you do exponents?)

This one's a unicode character. "²"

 

[Deleted member 54065]

Carefully.

 

[Lorelliad]

I didn't get a single thing