Fast Math Trick - Calculate the Cube Root of ANY number mentally! - Free Educational videos for Students in K-12

Fast Math Trick - Calculate the Cube Root of ANY number mentally! - By tecmath

Transcript


00:0-1	Good Day . Welcome to Tech Mouth channel . Now
00:01	the math trick video here . What we're going to
00:02	be having a look at in this particular video is
00:04	how to work at the approximate cube root of any
00:07	number instantly . You don't have to be perfect cubes
00:09	by the way . This is approximating any number ,
00:12	the q number of any number instantly . So sit
00:15	back and enjoy . This video is inspired by a
00:17	comment by red White G . I'm going to put
00:19	a link to this guy's Youtube channel in the description
00:22	below . Thanks a whole lot . So let's launch
00:24	into this . What's the approximation of the cube root
00:28	of say 87 ? I'll give you 10 seconds to
00:31	work this out . All right . And by the
00:33	way , this does not have to be a perfect
00:35	cube once again . But the same three numbers that
00:38	multiply to give 87 OK , 10 seconds . Pretty
00:41	much up . You should have worked it out by
00:42	now . Now , the approximation that I get using
00:45	my particular method , it's a little bit below 4.5
00:48	. It's probably about 4.45 Okay . But I got
00:50	around that up to about 4.5 anyway and you go
00:53	with that and you get around about that or are
00:55	close to you should be able to get within a
00:57	decimal places . So 0.1 or so difference if you
01:00	did . Congratulations if you didn't . Well , congratulations
01:03	. Also , it's your lucky day . I'm going
01:04	to show you how to do this . So that's
01:06	the couple of things before we start . First off
01:08	this particular tricks really handy if you have a running
01:11	knowledge of perfect cubes , what do I mean by
01:14	that ? Well , this is what I mean by
01:15	that too . To the power of three or two
01:17	times two times two is equal to or three cubed
01:20	is equal to 27 or four cubed is equal to
01:23	64 5 cubed is equal to 125 . 6 cubed
01:28	is equal to 216 7 cubed is equal to 343
01:33	8 cube is equal to 512 . So the more
01:36	of those that you know the better . Okay .
01:38	They're quite surprising that you actually are . We'll learn
01:41	that that pattern very , very quickly . But that's
01:43	the first thing . It's really , really handy to
01:44	know . The second thing is recognize that this is
01:47	an approximation . It's not exactly the exact answer .
01:50	You might want to use a calculator or something like
01:52	this . This is just a great mental exercise ,
01:54	you know , to work out the approximate of these
01:56	cube roots . So the way this particular trick works
01:59	is as follows . What I do for this particular
02:02	trick is I look for a cube root which occurs
02:04	below 87 The closest cube root below 87 you're going
02:08	to see here . But this is 64 64 the
02:11	cube root of this is equal to four . So
02:14	this forms the first part of our answer is four
02:16	. Okay , that's the whole number part of our
02:18	answer . The second thing we do is we are
02:20	going to look for the difference between 87 here and
02:23	64 87 . Take away 64 . You're going to
02:26	get this answer of 23 . This goes over one
02:29	marginal thing . We got to the third part of
02:31	our our answer here . I'm just going to show
02:33	you here . We're gonna use this whole number answer
02:34	here . I'm just going to put it down as
02:35	ex because we do a little bit of a process
02:37	to it . To this particular hole number , answer
02:39	We square it and multiply it by three . All
02:42	right . So four squared four times four is 16
02:46	times three is 48 . You work this out ,
02:49	you're going to see this is roughly a little bit
02:50	below 4.5 . That's why I said , you know
02:53	, it's a little bit between 4.44 point five .
02:56	The exact answer , We'll have a look is around
02:59	about 4.43 . So , as you'll see , it's
03:02	a fairly fairly great little method . As I said
03:05	, this is probably a little I guess this was
03:07	going to be a little bit below this , so
03:08	it's pretty close . And this is the exact answer
03:11	. This is the approximation answer . So how do
03:13	you go with that ? All right . So just
03:15	remember when you're doing this , the first thing you
03:16	do is going to look for a cube root beneath
03:19	the number we're looking for here . We're gonna look
03:21	for the difference between these two numbers and then we're
03:23	gonna go through this particular process here . So I'll
03:26	leave that up there and we'll go through another example
03:29	. Okay . All right . What about the Cube
03:31	root of 39 . Alright . You should be able
03:35	to go through and work that out . Maybe going
03:36	to pause the video . You don't have to give
03:37	yourself 10 seconds . Give yourself as much time as
03:39	you need . Okay . So what answer did you
03:42	get for that ? How would I go about doing
03:44	it ? Well , I go , okay . The
03:45	number below here , the cube number below is 27
03:49	. Okay , so 27 cube root of that is
03:53	equal to three . Obviously you don't need to write
03:55	this down , you can just go okay I'm gonna
03:56	three here , we've got this number at the top
03:58	. Here we look for the difference between these two
04:00	numbers , 39 take away 27 Is equal to 12
04:05	. The next thing we do is we go through
04:06	this particular process . This three squared three times three
04:10	is nine times three is 27 And this is the
04:15	approximation of a cube root . Here , you look
04:17	at this is this is round about 12 out of
04:20	24 behalf . So I'm gonna say this is a
04:22	little bit below that , this is probably around about
04:24	3.4 . Okay , not too bad . Right .
04:28	Uh the exact answer by the way , is 3.4
04:32	. So that's a really , really good approximation .
04:34	Right ? You go pretty good if you do like
04:36	this . I remember hit the like button , by
04:38	the way , I'm also going to put a link
04:39	up right now of a very similar approximation of how
04:42	you can go through and work out square numbers .
04:44	Okay , It's a very very similar process . Okay
04:47	, so that links coming up right now , but
04:49	what about in the meantime we go through a few
04:52	more examples . So I'll put a few of these
04:54	up right now . What about the cube root of
04:57	69 ? What about the cube group of ? Uh
05:03	What about 200 and 25 ? And what about the
05:08	cube root of ? Let's just go nice . Easy
05:11	number . Like 600 here . All right , so
05:15	go through , pause the video . So here you
05:17	go , see if we can work this out .
05:19	So the very very first one here . How did
05:21	you go ? Uh we have 69 here , 69
05:24	is a little bit below four here . So our
05:27	whole number answer is going to start with a four
05:29	. Okay , I'm just gonna put this 64 down
05:31	here . The difference you have here you're going to
05:34	see is five . Okay ? Now we just got
05:38	that last bit of the answer . We need to
05:39	work out four times four is 16 times three is
05:44	48 . You're gonna look at this and say okay
05:46	, this is roughly I'm gonna be under five out
05:48	of 50 so this is gonna be a little bit
05:50	around 4.1 , Okay , because this is about a
05:54	10th of this . Okay . And the actual answer
05:56	is 4.1 if you got that , congratulations . Okay
06:00	, let's have a look at the next answer here
06:02	. Okay to 25 , you're going to say this
06:04	is closest to six cubes , so let's put that
06:07	in . So this is six and you're going to
06:09	see here , this is 216 . Okay , so
06:13	Let's first off look for this difference here , we'll
06:15	look for this difference . You got 20-25 take away
06:18	to 16 . This is a difference of nine And
06:22	this is going to go over the final pile of
06:25	Iran to six times six , which is 36 Okay
06:29	then times three which is going to be 108 .
06:34	Okay . And this roundabout , you can look at
06:37	it and say okay , this is around about well
06:39	this is actually goes in 1 12 , this is
06:41	1 12 and he goes out perfectly . I'm going
06:43	to make life easy and call this lot . It's
06:45	going to be a little bit under 6.1 by the
06:48	way , the actual answer this is 6.8 So that's
06:52	a pretty good approximation . Right ? Mhm . All
06:55	right . The last question that we have here ,
06:57	the cube root of 600 . Alright , so 600
07:02	we go all the way up to eight here ,
07:03	so that's gonna be our Whole number part of her
07:06	answer . 512 is gonna be that's the eight Cube
07:10	is 512 . All right , the difference between these
07:13	guys , well that's gonna be 88 , that's going
07:16	to go over . Well this is gonna be a
07:19	bit harder now . Eight times eight is 64 64
07:23	times three is gonna be 100 and 92 . Okay
07:28	, this is probably the hardest part of this entire
07:30	thing when you do it . Okay . Because if
07:33	I'm approximately I tend to look at this and go
07:34	, okay , this is a round about half year
07:37	, it's a little bit less than half , I'd
07:38	probably say okay I was being pedantic here , I'd
07:41	probably say okay , my approximation is it's going to
07:44	be around about eight point 45 The actual answer that's
07:51	really , really close . The actual answer is 8.43
07:56	. So anyway , hopefully you like that particular trick
07:58	. Uh , and I didn't make a complete muppet
08:00	out of myself and the explanation by getting the wrong
08:02	answer anything like that . If I did comment and
08:04	keep me , keep me real honest , burned me
08:06	in the commentary there . Okay . Anyway , um
08:10	, like sub and while I'm at it , a
08:12	big shout out to all my patrons , uh ,
08:14	you know who you are and your support is really
08:17	appreciated on top of that . Once again , read
08:21	Y . T . G . Mate , thank you
08:23	for this idea . It's great . Okay . Anyway
08:26	, hope you enjoy this video . Thanks for watching
08:28	. We'll see you next time . Bye .

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Fast Math Trick - Calculate the Cube Root of ANY number mentally! is a free educational video by tecmath.

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