How to square any numbers in your head - fast mental math trick

My 8year old loves this! Thanks

Hey Siri.

the title says ANY number

Im a little confused(which doesn't take much! LOL!). Wouldn't it be just as easy to multiply 32X32? Wouldn't this be taking a lot of unnecessary steps? What am I missing?

What if the nearest ten you have to go up

I usually do it like this: Alexa, what is thirty two squared?' 😋

You complicated the whole lesson when you got to THE 77 exercise. Different method

I've thought myself this technique he used at the start of the vid which is actually pretty cool to see. I remember learning the formula for this from the middle school questions we had to find the maximum area of a quadrilateral and it turns out it was just a square shape. I know this sounds random but it's cool to see this application in a vid

really? you got to be kidding me... how about a 6 digits square? 567943^2 good luck multiplying this in your head pretty fast right? 567940 * 567946

Is there a way to express this as a formula?

because a^2 = a^2 -b^2 + b^2
= (a-b)(a+b) +b2
we can reorganize any number into this format with b being the small number

I watched this video when it first came out, and I have been using it ever since. What for? Nothing useful, but it's fun! And I've started doing the same method with three digit numbers now - it gets easy once you have done two digit squaring for 9 years.

Genuinely, finding this video again has brought on a lot of nostalgia.

I think now it's easy for me to calculate less than a minute

You can also do this trick with a 3 digit, a 4 digit, or even larger numbers....

The basic rule is this.
Take the number you are squaring.
Take everything except the first digit, and subtract from the number (e.g. 64 - 4, 128 - 28, 8192 - 192, and so on)
Take everything except the first digit, and add that to the number (eg. 64 + 4, 128 + 28, 8192 + 192, and so on).

Multiply the two values you got earlier (e.g. 60 x 68, 100 x 156, 8000 x 8384)

We then repeat this method, removing each digit (from left to right) as we go along.
E.g. for 128, after we do 100 x 156, we then do 20 x 36, and then 8 x 8.

And to prove just how quickly this works... let's go way overboard.
65536².

65,536 + 5,536 = 71,072
60,000 x 71,072 = 4,264,320,000

5,536 + 536 = 6,072
5,000 x 6,072 = 30,360,000

536 + 36 = 572
500 x 572 = 286,000

36 + 6 = 42
30 x 42 = 1,260

6 x 6 = 36

36 + 1,260 + 286,000 + 30,360,000 + 4,264,320,000 = 4,294,967,296

And yes, that is the value of 65,536².

The full calculation of what we're actually doing is:
[(65536 - 5536) x (65536 + 5536)] +
[(5536 - 536) x (5536 + 536)] +
[(536 - 36) x (536 + 36)] +
[(36 - 6) x (36 + 6)] +
[(6 x 6)]

but it is easier to multiply that two digit numbers instead of this method

48 × 50 2401

40 × 49 = 1960 + 81

49² 40×9 = 360+ 81= 441

isnt it easier to just times 32*32 rather than doing 30*34

1089

32²=(2⁵)²=2¹⁰ =1024

Another good method is
96²
=> 9² - 81
=> 6² - 36
8136
Then multiply 9×6×2= 108
Then add a 0 at the back of the no.
1080
Then 8136
+1080
=>9216
Only works with two-digit-numbers

I've said this before and ill say it again. Small channels are always better at explaining stuff. Im subscribing because of this video

You can do 30 x 34 but not 32 x 32????

Thanks 107 square is 11492

Nice trick find square

Yes find any number

Thank you

this means a lot and lot to me thx a lot

a^2 - b^2 = (a+b)(a-b)
change a bit:
a^2 = (a+b)(a-b) + b^2
let c = a+b
let d = a - b
to square 32 we need to:
round 32 to the ten's: 30
take the differnce: 2
now we substitute a = 32, b = 2
we calculate c = 34, d = 30
now, cd + b^2 is our answer

Before watching this, I would do 32^2 by multiplying 32 by 10, then multiplying than answer by 3, then adding 2×32 to that.
32 × 10 = 320
320 × 3 = 960
960 + (32 × 2) = 1024

Please cube or cube root

Multiply the two numbers and then times 2

Yes I do like it very much. Of course the same principle applies also to bigger numbers only the calculating gets a bit harder

For me, I just separate the numbers. So for example 57² I take 50 and 7 and multiply them each by 57. Which 50 x 50 = 2500, then 50 x 7 = 350 now add 2500 and 350 and we get 2850. Now 7 x 50 = 350, then 7 x 7 which is 49. Then we add 350 + 49 = 399. And now we fully add 2850 + 399 which then we get 3249. It sounds very complicated but it's actually easier than you think. As long as you know the multiples of the numbers by 5 and 10 then you're Gucci. It takes less than a minute to do in your head and is much easier than doing it manually once you've mastered it. I wouldn't say it's better than this, I'm just showing an alternative.

Wow, that's REALLY cool - all this time, I'd been using that good old-fashioned method: (a+b)²; However, honestly I prefer this method, thanks very much

THORRRRR

I don’t think this works for 16 or 17

66sqd can be converted to44x 99. 4400 minus 44=4356

32² = 1024 u can get the answer easily if u 32×32 🤓😕

5,920

5,929

1,080

1,089

1,020

1,024

why do you sound like thor

I have a huge question. Aren't you able to simple multiply for example.... answer for 45² is to multiply 45 × 45 = 45² which comes to 2,025.. I mean wouldn't that be the same answer just found in a simpler way?

daddy teacher :)