Best tricks for squaring numbers 1-100 mentally! | Math tricks - Free Educational videos for Students in K-12

Best tricks for squaring numbers 1-100 mentally! | Math tricks - By tecmath

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00:01	Good day . Welcome to take mouth channel . I'm
00:02	josh in this video . We're going to be having
00:04	a look at the best four tricks for mentally squaring
00:06	numbers in your head . So let's go now .
00:09	We're gonna start with a nice , easy general squaring
00:11	technique for numbers under 100 this is going to form
00:14	the basis of a couple of the tricks that have
00:16	come . So it's really worth paying attention to .
00:18	So let's just launch into this say I want to
00:21	square the number 23 so 23 squared and we'll see
00:25	what that equals . Now , this is a pretty
00:26	simple one to do once you know the trick .
00:28	So the first thing we're going to do is we
00:30	are going to look at the units number here and
00:32	we're going to see how far that is from the
00:34	nearest tens number . The nearest tens number is 20
00:37	. So this is Three from the nearest tens number
00:40	and we only use this three a fair bit .
00:43	The first thing we're going to do is we are
00:45	going to take three from 23 years , 23 take
00:48	three . We're going to get this answer of 20
00:51	. The next thing we're going to do is we're
00:53	going to add 3 to 23 . So three plus
00:56	23 is 26 . Now , what we're going to
00:59	do is we are going to multiply these guys and
01:01	this is not too hard to do because it's literally
01:03	26 times two times 10 . It's a pretty easy
01:06	1 . 26 times two is 52 times 10 is
01:10	520 . So 520 . Now where the zero goes
01:14	, I'm just going to leave a blank space And
01:16	this is now what we're going to do to get
01:18	the final number . We are going to square this
01:21	distance number here , this three , so three squared
01:23	is nine . The answer is 529 . Pretty simple
01:28	. Right ? So just to recap , how do
01:29	we do that ? So first off we looked for
01:31	the nearest tens number , which is 20 when we
01:33	saw how far 23 was from it , which was
01:36	three . And then we took three from 23 ,
01:39	we got 20 and then we added three , we've
01:41	got 26 . We multiply these two numbers and then
01:44	we added this distance squared sort of thing . So
01:47	it's pretty simple . It's a fairly standard technique we're
01:50	going to use again and again and again just with
01:52	a few little tweaks here . So let's go through
01:55	another example , bit harder now . So for our
01:58	next example , let's go 48 squared and we'll do
02:02	a similar sort of technique here . We're going to
02:04	look at the nearest tens number , which is 50
02:06	and we're gonna see that 48 Is to from 50
02:09	. So too is going to be the number we're
02:10	going to use a fair bit . The first thing
02:12	we do is we take two from 48 , so
02:15	we get 46 , we add 2 to 48 we
02:18	get 50 and now we're going to multiply these guys
02:21	46 times 50 . That's not too bad . That
02:24	is going to be 2300 . So we're gonna leave
02:28	those spaces there where we have those zeros for the
02:31	units number . What we're going to do is we're
02:33	going to square this number , So two times 2
02:36	is equal to four . So the four is going
02:38	to go in here . So that's just gonna be
02:40	zero before our answer . 2304 . Easy . Right
02:45	? So that's the first trick for squaring and that's
02:48	for any number under 100 . But what about And
02:51	this is where we're going to get to the second
02:53	trick . What about if we have It's another number
02:56	under 100 . But say I was to consider the
02:59	number like 75 and I wanted to square that Now
03:04	, you might say , Okay , well is 80
03:05	closer or is 70 close ? And how do we
03:08	deal with that ? Well , so finally enough numbers
03:11	ending in five or even easier to square the number
03:14	is not ending in five . And this is how
03:16	we do these in this case . What we do
03:18	is we look at the tens number . Okay ,
03:21	so the tens number here is a seven for 70
03:23	and then we look at the number after that and
03:26	we're just going to multiply these 27 times eight .
03:28	And this is going to give us the first part
03:30	of our answer which is 56 . The last thing
03:33	we do is we basically add a 25 to this
03:36	, which is five squared 56 to 5 now .
03:39	Really ? What just went on then ? So this
03:41	is the trick . That's all we've got our answer
03:43	. But what just went on now , as you
03:45	can see if I was to say the nearest number
03:47	I could say , okay , we'll say I was
03:48	to add five to it . You can see that
03:51	if I add five to it , I'm going to
03:52	end up with okay , so first off I take
03:55	five from it , I'm gonna go 70 I'm gonna
03:57	add five to it , I'm gonna go by 80
03:59	and that's where our seven eights are , 78 to
04:01	56 . And then we just end up with five
04:02	squared which is the 25 on the end , so
04:05	it's the same sort of trick again , but a
04:06	simpler one . Okay , let's just go through another
04:09	example of this . Okay , we'll go through a
04:11	couple of these . What about we do 45 squared
04:15	. So nice and simple . Let's just have a
04:17	look here and go , okay , the next number
04:19	up from four is five , so four fives a
04:22	20 then we just put five squared on the end
04:25	. 25 2000 and 25 . Really ? Basic .
04:29	Right ? I didn't bother of that one out .
04:31	I just put a nice another simple one up here
04:33	, a bit of a bigger one there . What
04:34	about 100 and 15 squared now , what are we
04:38	going to get for this ? Okay , so if
04:40	we have a look at this entire party at 11
04:43	and the next number is 12 , 11 times 12
04:46	Is 130 - 132 . Once again , we just
04:51	put 25 on the end . Right ? So there
04:53	we go . That is the second trick . Okay
04:56	, so we've done the first trick which is looking
04:58	at any number under 100 . And now we've just
05:00	looked specifically at numbers ending in five . Let's have
05:04	a look at a third trick . So for our
05:05	third trick , what about squaring numbers near 100 ?
05:08	Well , there is a nice easy way to do
05:10	this as I'll show you in my third great squaring
05:13	trick . And an example here is 107 squared .
05:18	Now the way that we do these these as follows
05:22	. Now you're going to see a very , very
05:23	similar pattern . First off , how far is this
05:26	to the nearest tens number ? Let's not go to
05:28	the nearest tens number . Let's go to an easy
05:30	tens number , which is 100 it is seven from
05:34	100 . So what do we do first off we
05:36	subtract seven from 107 . We get 100 and this
05:40	is going to be multiplied by seven plus 107 which
05:44	is 100 and 14 . That's really , really easy
05:46	. Right ? That's just going to be 114 with
05:49	these two blank spaces for where the zeros could go
05:52	. Now what we do is we square this particular
05:55	number like we've done every other time Seven squared is
05:58	equal to 49 . So there you go . 11,449
06:04	. Pretty simple . Right ? What about to do
06:06	another one which is above 100 I'm going to go
06:09	to one which is just below 100 . What about
06:11	for our next example we do 105 squared and we
06:15	see what this equals 105 square . We can treat
06:18	this like a number that ends in five . We
06:20	could go , okay , the next number after 10
06:22	here is equal to 11 . 10 times 11 is
06:26	100 and 10 with 25 on the end . Or
06:29	what we could do is we can say , okay
06:30	, this number is five from 100 . So 105
06:34	plus five is equal to 110 and then we square
06:38	this number and we get the same result . Either
06:41	Either way , it's pretty simple thing . Right ,
06:43	Okay . What about ago a number under 100 .
06:46	What about we look at the number 97 and we're
06:49	going to square that and we can do this pretty
06:52	quickly . This number is three from 100 . So
06:56	first thing we're going to do is we're going to
06:58	subtract three from this and we're going to get the
07:00	number 90 for this is going to multiply by 97
07:04	plus three , which is 100 . So 94 times
07:08	100 . Well , that's pretty simple . That's just
07:10	going to be 94 with two spaces after it .
07:13	Then what we do is we square this distance number
07:16	again . So three times three is equal to nine
07:19	. That's our answer . 9,409 . Hey , like
07:24	I said , it's just a derivative of is the
07:26	same idea each time . And it's a pretty simple
07:28	idea . It's not always as easy for every single
07:31	number . And once you get right above 100 like
07:34	, you can get into 100 and 20 or 100
07:36	and 50 it does get more and more complex just
07:39	as you would expect . Okay , I'm not gonna
07:40	pretend there's a silver bullet with those . That makes
07:42	it really , really simple . Once the numbers get
07:44	more complicated , you know , the mental gymnastics also
07:48	gets a little bit more complicated now , for the
07:51	fourth particular trick ? Well , I'll show it to
07:53	you right now . Now , the fourth squaring trick
07:57	is a nice , easy but not particularly useful squaring
08:00	trick , but I do like it . And it's
08:02	this one here . Say we consider one squared .
08:05	Well , that is equal to 11 times one is
08:07	equal to one . What about 11 square while 11
08:10	times 11 is equal to 121 . Okay , Now
08:16	111 squared . Well , I don't know . Put
08:19	this indeed calculator or work this out . This is
08:22	123 to 1 . You can sort of see here
08:26	. 123 to 1 . We go up we go
08:28	down , there's three numbers here , and that's the
08:30	point we sort of hit here , so we can
08:33	keep going on this one . And we could say
08:34	, okay , what is 11111 square . We have
08:39	five once . What's the answer ? This going to
08:41	be ? Where we're going to go up to the
08:43	number 512345 and then back down to one . The
08:46	answer will be 12345 4321 . And that's just a
08:55	great little trick . Like I said , not largely
08:57	useful , but it's a cool little trick nonetheless ,
09:00	for squaring numbers with one , you know , very
09:03	, very specific . Like I said , not particularly
09:06	useful . All right . So hopefully you're paying attention
09:08	there and I'll tell you what you better be because
09:10	now I'm going to give you a test just to
09:12	see how you go . So I'm gonna give you
09:14	a number of these square questions . So here you
09:16	go . Use any technique you've just seen there to
09:18	try and solve them . So the very very first
09:20	one . What about we do 106 squared the next
09:24	one . Let's do 65 squared The next one .
09:28	Let's go 20 seven squared for the next one .
09:32	What about 1111111 squared . We'll see how that goes
09:38	. That's a pretty big one . I reckon you'll
09:40	be all right ? So pause the video , give
09:42	this a go . But I reckon you'll be able
09:43	to do these just as fast as I can answer
09:46	them right now . So the very very 1st 106
09:48	squared . So this is six from 100 . So
09:51	we're going to add that on top of so 106
09:54	plus six . This is equal to 112 . And
09:57	then we're going to square six here . 6 6
09:59	is 36 . That's 11,236 , 65 squared . Nice
10:06	and basic . Alright . The next number after six
10:08	here's a 776 is 40 to 42 with the 25
10:12	on the end 4225 . The next one is 27
10:18	squared . Now I've adapted this one a tiny little
10:21	bit because to tell you the truth , I'd prefer
10:23	to multiply by twenties and I do my thirties .
10:25	They're not much harder , but it's just something I
10:27	personally prefer . So let's do that . So I
10:29	am seven above 20 here . So let's multiply 20
10:34	Multiplied by whatever seven plus 27 is which is 34
10:39	. You're going to see twenties are really amazing to
10:41	multiply for . We're just was doubling okay with a
10:44	10 on the end . So this is basically going
10:46	to be 680 then we're just going to square 777
10:51	49 . So we're gonna add 49 to our answer
10:54	. All this you can do in your head .
10:56	The answer will be seven to Don't . Alright .
11:01	And last of all , 1111111 That number there is
11:07	1,111,111 . And we're squaring that we have 1234567 ones
11:15	. So we're going to go up 123456 seven And
11:22	now we're going to go down again 654-321 . And
11:29	that's a really , really big number that we have
11:31	there . Let's see if we can read this .
11:34	Okay , what we have here is 1,234 billion 567,654,000
11:44	321 . Okay , so anyway , so how did
11:47	you go with those ? Hopefully that was not too
11:49	bad . Okay , you can see that you can
11:51	kind of adapt as you go along with these .
11:53	As long as you've got those key ideas going Anyway
11:56	, they are my favourite four ways of squaring numbers
12:00	and I hope you like them . I hope you've
12:01	seen these before . Maybe I just give you a
12:03	bit of a refresher either the first time you've seen
12:05	them . Well , you know , they're pretty cool
12:06	. Right ? Anyway , if you like this video
12:09	, give us a thumbs up and put in the
12:10	comments what you thought of the video . Thank you
12:12	for watching and we'll see you next time . All
12:14	right , Bye .

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