Math Is Fun Forum

4DLiVing

Member

Registered: 2011-01-08

Posts: 22

Square any two digit number in your mind!

Here is something interesting that I have been using to amaze my 8th graders~!

I have them pick a two digit number and I will square it in my head...

Here is how I do it...

(a + b)² = a² + 2ab + b²

Say they pick 24; 24 is (20 + 4); a = 20 and b = 4 so...

so 20² + 2(20)(4) + 4² = 400 + 160 + 16 = 560 + 16 = 576.

This works for all two digit numbers.

Look at 49 (this ones a little tougher to do in the head but if you practice, you will master!)

40² + 2(40)(9) + 9² = 1600 + 720 + 81 = 2320 + 81 = 2401

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square any two digit number in your mind!

Hi;

For numbers like 49 which are under but close to a nice number I use

Now all you have to do for 49^2 is a = 50 and b = 1

50^2 - 2(50)(1) + 1

2500 - 100 +1 = 2401

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

4DLiVing

Member

Registered: 2011-01-08

Posts: 22

Re: Square any two digit number in your mind!

aha! very cool... i like it a lot!  That'll save me a few seconds!  Thanks for the other side of the box!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square any two digit number in your mind!

Hi 4DLiVing;

You can also use that identity to multiply lots more, for instance 84 * 76.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

4DLiVing

Member

Registered: 2011-01-08

Posts: 22

Re: Square any two digit number in your mind!

84 * 76
would be (a + b) (a - b) = a^2 - b^2

or (80 + 4) (80 - 4) = 80^2 - 4^2 = 6400 - 16 = 6384.

Nice! 

This does require a more "specialized" starting position with the numbers that are given to me, but I shall remember this one as well!

Thanks bobbym!

I have tried (a + b + c)^2, but I think I would need more of a ram upgrade in my brain in order to do these in my head.  Nonetheless, I always found it interesting how these expansions can make our lives easier!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square any two digit number in your mind!

Not really computers make our life easier by allowing us to concentrate on the important things in life like eating.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Square any two digit number in your mind!

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