Cube Trick - work out cubic numbers (1 - 100) fast! - Free Educational videos for Students in K-12

Cube Trick - work out cubic numbers (1 - 100) fast! - By tecmath

Transcript


00:0-1	Okay , welcome to the Tech Math channel . What
00:01	I'm gonna be having a look at this video is
00:03	a way of cubing any number between one and 100
00:05	. It's a really nifty little trick and I'll show
00:09	it to you right now . Anyway , let's start
00:11	first off , I'm going to get you to try
00:15	and cube this number here . Now . I'm guessing
00:18	the way that you'd usually do it is this way
00:20	you get 31 and you go 31 times 31 times
00:26	31 . And eventually you would get your answer .
00:29	Okay ? But the way I'm going to show you
00:32	right now is just a different way of doing it
00:34	. Okay . It's a really good little trick .
00:37	I find it's not instant . I'm not going to
00:39	not going to lie to you and say that ,
00:41	but it's a great little trick nonetheless . And the
00:44	way it works is this , so we call ,
00:47	we basically get these numbers here , the three and
00:50	the one and we give them letters , letter names
00:56	. Okay , for the first number here and be
00:59	for the second number . Okay . And there's a
01:02	bit of a pattern to how you work these out
01:05	. So first off what we do is we're gonna
01:08	get a are we going to cubit then ? What
01:11	we're gonna do is we're gonna get a we're gonna
01:13	square in times of I . B . We're going
01:16	to get be we're going to square it in times
01:18	of by A . And then we're gonna be we're
01:21	gonna cubit almost ran as spicy . Okay then what
01:26	we're gonna do is we're gonna double these two numbers
01:29	so we in effect we have to a squared B
01:33	. And two B squared . I okay now straight
01:40	away you're going to be looking at going that's not
01:42	simple at all . It's something you do get used
01:44	to and it's not as bad as it first appears
01:47	but it's a good little trick . Okay just bear
01:50	with us . So first off a cubed A is
01:53	three so three cubed . I'll start writing it over
01:56	here . It's 27 . I'll put it over here
01:59	. A squared times be okay . I squared is
02:02	nine times B bees one . So nine times one
02:06	is nine . The next one , B squared one
02:09	squared is one times i is three . And then
02:14	we end up with b cubed be cubed here one
02:17	times one times one . We end up with a
02:19	one there . Okay . And then it's these numbers
02:23	here that we doubled . Okay so nine doubled is
02:28	18 And three doubled is six . Then simply what
02:33	we do to get our answer is we add these
02:35	numbers together . Okay So one plus nothing is 13
02:38	plus six is 99 plus eight is 17 , carry
02:41	the one these all together . It's not . And
02:46	to there so we have the answer . 29,791 .
02:50	It's pretty cool trick . Right ? I'll tell you
02:53	what , I'll go through a couple more examples .
02:56	So we'll get rid of those ones . I'm going
02:58	to keep the other stuff up there . Okay ,
03:00	I've got these over here just to help us out
03:02	a little bit , as I've said in another video
03:04	. I look I reckon these are really handy to
03:07	to learn . They only take you possibly , you
03:10	know , three or four minutes to learn tops .
03:12	Yeah . And then they allowed to do a whole
03:15	bunch of different things , like working out cube roots
03:18	. Uh for numbers right up to have who have
03:20	Cuba . It's right up to 100 as you'll see
03:21	my other videos as well as working at the cubes
03:24	, numbers for numbers up to 100 . So it's
03:26	a really handy if you just know these particular ones
03:29	here . Uh Okay , let's have a look here
03:32	. So let's do a different example . Ah Let's
03:34	do a bigger number now actually , we'll do a
03:37	smaller number . Let's do 23 Cubed . Okay ,
03:42	I probably should move this number . I'll get it
03:45	and I'll move up here and let's start doing our
03:49	23 Cubes . So A and B . Okay .
03:53	So I cubed is right ? Yeah . Ah We
03:59	have a squared which is four times three which is
04:04	12 . Okay . Remember that little 12 ? We
04:08	have B squared Which is nine times 2 which is
04:14	18 . Then what we have is we have be
04:19	cubed which is 27 . All right . And then
04:22	we double these numbers here . I gave you remember
04:25	first off we had a 12 . I'm gonna double
04:27	that . We get 24 . Okay , that's 12
04:30	there . You line it up with that two finishes
04:32	and that's where that fall be . So the two
04:34	is over here and here . I double the 18
04:36	. So the six will go here and we're going
04:39	to end up with a three . He because double
04:42	18 is 36 . Oh man , I'm really going
04:45	to be squashed on the bottom of the video screen
04:46	this time . I'll tell you what I'll do is
04:48	the whole movie is down a bit . How does
04:50	that go ? Probably probably be better . Okay .
04:55	All right , so let's add these up . Seven
04:59	, two plus eight plus six is 16 , carry
05:02	that one . Then what we get is we go
05:04	one plus one plus two plus four plus three is
05:07	11 carry the one . One plus one plus eight
05:11	plus two is 12 . That's our answer . 12,167
05:17	. Yeah . Okay , one last example . Yeah
05:22	. Okay . Uh Now what we'll do is I'll
05:27	give you a bigger number this time and as you
05:29	can imagine , the bigger the numbers they do get
05:31	a little bit more tricky . Okay , if you
05:33	get into 96 and things like this they do get
05:35	a bit more tricky . I'm going to do 45
05:38	cubed . Okay , so I'll start doing it here
05:42	. So a actually what I recommend , pause it
05:46	, see how you go , pause Now work through
05:49	the answer . Okay so a cube four cubed .
05:52	I've written them over here again . They're really worth
05:54	knowing . We have 64 . Okay then what we
05:58	have is we have a wait a second , A
06:01	squared B . We have that 16 times 5 .
06:05	16 times five is 80 . Yeah . Then what
06:11	we have is we have a B squared A .
06:13	So 25 square five squares 25 times four is 100
06:18	. Now look that 100 I'm gonna put that zero
06:20	there , that zero there and that one right all
06:23	the way up there . Okay , Who then what
06:27	we're gonna do Is we get finally be cubed be
06:32	cubed as five cubed is 125 . Okay . I'll
06:36	put the two there And as long as it's landing
06:38	somewhere in those in this this right bits , it
06:41	doesn't particularly matter . It doesn't matter if you put
06:43	the number that one down there and said it's all
06:45	going to get out into the same bit of pie
06:47	. All right . So the next thing we do
06:50	is we double these numbers , if you remember ,
06:51	what was it that one before ? Was an 80
06:54	? So we double that . Okay , the finished
06:57	here , so we get the number 1 60 then
07:02	what we do is we double this double here ,
07:03	which was 100 . Would double it to get 200
07:07	. Okay . And we add these up . So
07:10	five two one , this one's one plus eight is
07:18	9 13 , 19 21 , carry the two .
07:23	And then we end up with six plus two ,
07:27	which is eight plus one , Which is nine .
07:29	And that's our answer 91,125 . It's pretty cool .
07:33	Right ? Anyway , and also put up a video
07:36	where you can work out these numbers if this is
07:38	a one . As you can imagine , it gets
07:40	a little bit easier because there's a few little things
07:42	you don't have to do , but it's a really
07:45	great little trick and a few people are gonna go
07:46	, hey , wait a second , this is just
07:47	playing around with a few algebraic techniques and you know
07:50	what ? You're right . But look , don't tell
07:53	anyone . Just pretend it's a it's a really nifty
07:55	little trick . In fact , I actually quite like
07:57	relating to algebra as well , which we will be
07:59	doing in future videos . We're gonna start having a
08:01	look at algebraic stuff . Okay . Uh , anyway
08:04	, I hope you like that trick . I'll see
08:06	you next time .

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Cube Trick - work out cubic numbers (1 - 100) fast! is a free educational video by tecmath.

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