Square ANY number up to 1000 in 5 seconds - math trick! - Free Educational videos for Students in K-12

Square ANY number up to 1000 in 5 seconds - math trick! - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Math Channel . I'm
00:01	josh . Let's try all around the internet the other
00:03	day . And I saw this particular trick for squaring
00:06	numbers up to 1000 . So I thought I'd share
00:08	it with you . So let's just get straight into
00:10	this . So how fast can you square the following
00:13	number without a calculator . So I'm going to get
00:15	you to work out 403 square now . You can
00:19	use pen and paper for this . Go okay .
00:24	I reckon I'm gonna start right about now solving this
00:26	and we'll see how I go . So 16 0009
00:31	and then I'm going to get 12 . I'm gonna
00:33	make it 24 . And then I got my answer
00:35	which is going to be 16 24 09 And that's
00:41	how fast you can square numbers . Using this particular
00:44	method , it's pretty cool one . Right ? So
00:46	how did you go ? I'll tell you what I'm
00:47	going to get back to this one and then you
00:49	can see if you can do it as fast .
00:50	So I'm going to show you this technique for squaring
00:53	numbers up to 1000 but before we get there ,
00:56	okay , I'm gonna show you a couple of the
00:58	smaller numbers first . Just let's walk before we can
01:01	run , so to speak . Trust me , it's
01:03	better this way . So anyway , I am going
01:05	to come back to this 1 , 403 . I
01:07	promise I will , But I'm just going to go
01:08	through a couple of other ones . First couple of
01:11	smaller ones . So I'm going to start with this
01:13	particular problem here . What about we do 67 squared
01:18	? Now , the way that this particular technique works
01:21	is as follows . Now it does all the same
01:23	calculations is traditionally squaring where you go 67 times 67
01:27	to work it out . But it just puts things
01:29	in a more convenient , coherent sort of order ,
01:32	where you can do them a whole lot faster .
01:34	So the very , very first thing we do is
01:36	we are going to square this first number here ,
01:38	so six squared is equal to 36 . I'll put
01:41	that down . The next thing I'm gonna do is
01:43	win a square seven here says seven squared is equal
01:46	to 49 . The next thing we're going to do
01:49	is we're going to multiply these two digits six times
01:52	seven . And we're going to multiply then our answer
01:54	by two , so 67 to 42 , double that
01:57	times by two is equal to 84 . Now all
02:01	the same calculations that usually would occur have occurred ,
02:04	but they just occurred in a separate order . Now
02:06	what we're going to do is we're going to add
02:08	our answer together . So when we do this ,
02:10	we're straight away . What we get is this is
02:13	a 94 plus four is equal to 86 plus eight
02:17	is equal to 14 . So we carry the one
02:19	there and three plus one is equal before you go
02:24	. And that's how this technique works . There is
02:25	a bit of a tweak for our bigger numbers .
02:27	So I'll get to those in a second , so
02:29	I'll keep that up there . Let's go through a
02:30	bit of a quick recap what we did and then
02:32	I'll give one for you to have a go to
02:34	and then we'll get to these big three digit numbers
02:36	. Right ? So the first thing is we square
02:37	this first digit 66 36 . The second thing we
02:41	square the units digit here 7 7 - 49 .
02:45	And then we're going to multiply these two digits and
02:48	then multiply that by two we got 84 then we
02:50	added the whole lot together . Pretty simple . Okay
02:53	, so what about I give you one of these
02:55	? I'm going to keep this one up here so
02:56	you can guess you refer back to that . And
02:59	what about we do 82 squared . A nice easy
03:02	one . So give it a go now I'm going
03:05	to go through it . Okay , so eight times
03:07	eight is equal to 64 . Two times two .
03:11	We're going to put that down as a two digit
03:12	number is 04 The next one . We multiply these
03:16	two digits and then we double our result Two times
03:20	eight is equal to 16 . We double that .
03:21	We get 32 . Yeah . And now what do
03:24	we do with final step ? We add all our
03:26	answers together and this one we can just add directly
03:29	over . So 6 7 2 4 , So how
03:36	did you go with that ? Pretty all right .
03:38	I'll tell you what now . It's a big are
03:39	the big kahuna burger I guess . And we are
03:41	going to get ourselves into three digit numbers . How
03:44	to do this with three digit numbers . Okay .
03:47	The biggest one I guess you probably pick up from
03:48	this is if you have something like a four of
03:51	your answer a nine , put it down to 0409
03:54	that does matter . Okay , so pretty simple .
03:57	Let's go through and do three digit numbers . Now
04:00	. The way I'm gonna do this is I'm going
04:01	to go through the first one . We're going to
04:02	show it to you and how I would approach is
04:05	then I'd give one for you to do . And
04:07	then I'm gonna show you that one from the very
04:09	start there and we'll see how we are go with
04:11	it . So anyway this is much the same as
04:14	that first part we did but with a couple of
04:16	tweaks . So let's just start this out straight away
04:19	. So what about the example of 512 squared now
04:23	? How would I go about doing this ? Well
04:25	first off we're just gonna go through and square each
04:27	one of these digits here . So five squared five
04:29	times five is 25 one times one is equal to
04:33	one . Which we're gonna write down 01 and two
04:36	times two is equal to four . We're gonna write
04:37	this down as 04 The next thing we're going to
04:41	now multiply these two digits and double it and we're
04:45	going to multiply these two digits and double them and
04:47	put down the results of five times one is equal
04:50	to five times two is equal to 10 . So
04:53	I'm gonna put that down right here , and two
04:55	times one is equal to two . And then we're
04:58	gonna double that and we get the answer of four
04:59	. All right , pretty simple . And last of
05:02	all , we have to do one extra step .
05:04	We're gonna be multiplying the two by the five here
05:07	. Okay ? So two times five and then we're
05:09	gonna double that answer as well . We're gonna dump
05:12	the answer right in the middle here . So Five
05:14	times two is equal to 10 and then double that
05:16	. You get the answer of 20 . All right
05:20	. So now what do we do ? We're gonna
05:21	add all these together . And if we can just
05:23	do this straight down nice and easy and let's do
05:25	that . So this is going to be a 25
05:27	plus one is 60 plus zero plus two is equal
05:30	to 21 plus zero plus zero is equal to 10
05:34	plus four is equal to four . And this one
05:37	is also going to be for our answer is 260
05:40	. 2000 . 144 . And as you'll see ,
05:43	we didn't get away with not doing any of the
05:45	calculations here . We just did them in a different
05:47	order . It's just a different technique for doing it
05:50	. You may or may not use it like anything
05:51	in life . So what about I give you an
05:54	example to do for yourself right now ? And then
05:56	I'm gonna get to that first example . If you're
05:57	going to see these are really , really , really
05:59	quite simple to do . I did choose that one
06:01	specifically by the way . So what about to give
06:04	you one of these ? I'm just gonna pick a
06:06	random one here and hopefully get the answer . Right
06:08	. What about we do 362 . Alright . Made
06:13	this quite a bit harder . Right , bigger numbers
06:15	. I chose a nice easy one for myself to
06:16	use a hard one for you . Better you look
06:18	the fool than me . Right ? So let's get
06:20	the first numbers here . So we square three .
06:22	We get the answer of nine . I'm gonna put
06:24	down to 09 I know we don't need to but
06:27	it might help with the placement in a little bit
06:28	. We're gonna square six . Next we're gonna get
06:30	this answer of 36 they were gonna square to get
06:33	the answer of four . Okay , now what do
06:36	we do ? We're gonna multiply these numbers and then
06:38	double them three . Sixes are double that that's going
06:41	to be 36 6 to 12 , double that .
06:45	We're going to get 24 last of all , 3
06:49	to 6 , double that we get the answer of
06:51	12 . And we just go through now and at
06:54	these I reckon I am going to do this right
06:57	to left . So we're gonna get a four here
06:58	. Zero plus four is equal to 46 plus two
07:01	plus two . That's equal to 10 carry that one
07:03	there . Three plus six is equal to nine plus
07:06	one is equal to 10 . Plus one . Is
07:08	equal to 11 , carry that one . And then
07:10	we're gonna get one plus nine is equal to 10
07:13	plus three is 13 . 131,000 And 44 . So
07:18	how did you go on that ? Did you get
07:19	that answer ? Well , it's not a bad technique
07:22	writes a pretty simple one to do . So now
07:24	I'm going to show you the example from the very
07:25	start . Okay . The question from the very start
07:28	, you thought I would have got to that one
07:29	first , but you gonna leave you hanging for something
07:31	, right ? And let's put this one down .
07:33	403 squared . I reckon you we are given a
07:35	fair fly now and give it a go and see
07:38	how far she can do it . But I'm gonna
07:39	tell you what makes this easier because we have multiplication
07:42	by zero . It makes some of these calculations really
07:46	basic . So four squared is equal to 16 ,
07:48	0 squared 00 and then three squared is equal to
07:52	nine . There you go . The next one we're
07:54	gonna multiply these guys and then we're gonna get zero
07:57	. So we don't have to worry about we're gonna
07:58	multiply these guys , we get zero so we don't
08:00	have to worry about . The only way we have
08:01	to worry about is four times three and doubling that
08:04	. We're gonna dump that right in the middle for
08:05	3 to 12 . Put the 24 there . And
08:08	as you can see , I can just add these
08:10	straight across 162409 And we have our answer right ?
08:17	These ones where they have a zero in the middle
08:19	. Really basic to deal with . But I'll tell
08:21	you what I'm going to give you one of these
08:22	. Then you can feel really , really smart about
08:24	yourself and why not ? You've learned something today .
08:26	You should feel smart about yourself . I'm gonna give
08:29	you one . Okay ? The one I'm gonna give
08:30	to you zero in the middle . 607 squared .
08:34	Alright . And see he should be able to do
08:36	this pretty quickly . Or you can you can almost
08:38	do this directly . In fact , I am going
08:39	to try that and I haven't tried this before .
08:41	So this is gonna be live . So I screw
08:43	up Well , I'll probably end up this out ,
08:45	but I don't think I will . So six times
08:47	six is equal to 36 . Now we know that
08:49	that zero here is going to put two zeros in
08:51	the middle . So let's just work at this middle
08:53	part 1st 67 to 42 double that . We're going
08:57	to get the answer of 84 . We know we're
09:00	gonna be adding that on . So let's just do
09:01	that right now . Then seven sevens are 49 .
09:05	A pretty crazy , right ? We have ourselves our
09:07	answer straight away . Hey , I reckon that work
09:10	. That was pretty cool . I'm gonna give one
09:12	more of those ago . So let's go Nice ,
09:14	easy one . Let's go 306 squared . And I
09:19	know you're kind of looking to go , you're choosing
09:21	easy ones . Hey , they're all pretty easy .
09:22	Right ? When you really look at it , they're
09:24	not that bad . So three squared is equal to
09:26	nine now , I'm not even gonna put the zero
09:28	there because I know I'm not gonna be playing with
09:29	that later . 00 is gonna give me zero .
09:32	So I'm going to worry about this , this part
09:33	here . Three times six is equal to 80 double
09:36	that going to get the answer of 36 then 66
09:39	is 36 years . Our answer 93,636 . Anyway ,
09:46	that's a great little technique that I are spotted .
09:48	I thought you might be really interested in knowing and
09:50	if you like it , give me a thumbs up
09:51	, put in the comments , you gonna be probably
09:53	telling me things like , hey , this is just
09:55	doing exactly the same calculations , but just in a
09:57	different order . Hey , I told you that already
10:00	, right . It's exactly what it is okay with
10:02	that . You often can't get away with doing the
10:04	calculations you have to do . Sometimes it's about working
10:07	them in a smarter order . So in a big
10:09	shout out to my subscribers and patrons and all your
10:11	people who have watched and stuck with me this far
10:14	, um , you take care of yourself and we'll
10:17	see you next time . Bye .

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