Fifth Root Trick - Numberphile
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- Опубліковано 14 лют 2014
- A neat trick to quickly calculate fifth roots.
More links & stuff in full description below ↓↓↓
Featuring Simon Pampena, Australian Numeracy Ambassador.
/ mathemaniac
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NUMBERPHILE
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Euler was such a badass. His work is everywhere.
There's a joke that says all things in math are named after the second person that discovered them, because the first one was always Euler
Yeah… .
@Alexis Hazel DeSilva They truly were astonishing.
Hes no joke hes a real genius
He definitely was, but I wonder how much of that was because simply not that many people were able to study mathematics at and before his time.
Ah the classic 69^5
5 parties of 69 bro
Tom Stack genius
of course they would do that
"That was a bit hard, but I got used to it."
... Yeah.... I bet. >__
A timeless classic
Dude looks like an evil genius waiting for you to say that big number.
😂!!!
My wife's name is Anushka Sharma
@@ViratKohli-jj3wj I dont get it
I knew this trick with the third root. There for the last digit you have to swap 2 with 8 and 3 with 7 (and the other way around) and all the other are the same in the last digit.
Same. Square roots too, but you need to do more work since all last digits have 2 possibilities
Natürlich guckt DorFuchs Numberphile...
Hahaha, DorFuchs du pussyslayer :D
DorFuchs p
ja DorFuchs!
This channel is simply one of the best to ever come out on UA-cam. The amount of time I spend watching these videos is profane.
Dude interviewing the other guy, if you turn your phone sideways you can use the scientific calculator to get 38^5 directly.
+Numberphile nice attempted save
+Srcsqwrn I'm fine with you being fine with this.
Android says square root 2 x2 is 2.8 so it's not number phile approved😃
sqrt(2)^2 = 2, not sqrt(2)x2 :)
I'm disapointed, rip maths
This dude's cool, get him here more often!
Check out his "Epic Circles" contribution. Just fascinating...
Why is there a deer walking around in the background?
Hero of the Beach Because it was open season on Mathematicians.
That's Lulu. Brady's dog.
no, its a cheetah.
how did i not notice that xd
That's dinosaur..-(1000x) smaller😂😁😂😁
When he said, “How’d I do it so quickly?” I said to myself, “Cause your a genius.” Only to immediately hear him say, “Cause I’m a genius.”
He truly is a genius!
5:47 "a lot of kids loved 69 to the power 5" haha, those sassy kids :D
it was a bit hard but i got used to it
XD
There is a trick similar to this with cube roots, and at one point i just remembered the number for 69^3...
This guy is my favorite of all the people you interview. He won me over when he split my brain in half about the number line in one of your previous videos.
This video is fantastic.
Euler never seems to stop impressing me... from 300 years ago
Every time I hit "like" when the number was originally Prime, I feel slightly bad.
I love EULER
He's made of you anyway
StubbornAtom oiler*
I started laughing so hard about the 69 thing.
electrocat1 Liking this comment would be wrong...
I waited for 69 likes for so long!
at 3:25 I thought that was a deer behind him. LOL
Same lol?
Doggi
Lulu passed away sometime this year iirc. R.I.P. );
Time to look incredibly clever in front of my friends!
Do it!
And fail miserably and get embarrased in front of ur friends
You mean your top 10 friends?
not to be that guy 6 years later but I feel like intelligent would he a better word
I've now watched every single numberphile video. Binge watched them over the past week. Nice work Brady! Doing the same now for your other channels :P
Locut0s do you still watch them?
Video should end at 1:43 lol
Your likes ended at 143 lol
Orbrun, right now 205.
And growing: 214( not mine because in this prospective It may have ended at 1:39).
304 likes
314
Wow! Time to go win some bets!
Mentally calculating 20^5 is easy: just apply the distributive property to exponentiation the same way you would with multiplication: 20^5 = (2 * 10)^5 = 2^5 * 10^5 = 32 * 100000 = 3200000
30^5: 3^5 = 9 * 9 * 3 = 81 * 3 = 3(80 + 1) = 24 * 10 + 3 = 243 = 24300000
40^5 = (4 * 10)^5 = 4^5 = 16 * 16 * 4 = 256 * 4 = 4(200 + 50 + 6) = 800 + 200 + 24 = 1024 * 10^5 = 102400000
That's all mental calculation, except I have a trick for 4^5. I know that sqrt(4) = 2, so I can just double the magnitude and get 2^10, which I happen to know is 1,024. Or you can square 4, subtract 1 from and halve the magnitude to get 4^5 = 4^4 * 4^1 = 16^2 * 4
Brilliant 😍
The same works for cubing/taking cube roots you just need to remember the answers to 1-9 cubed. The difference is that if the last digit is an 8 (e.g 74088) the last digit of the number you've cubed is 2 and vice versa (in this case the answer is 42) and if the last digit is 7 then the last digit of the number you have cubed is 3 and vice versa.
I had a math pattern I found when in freshman year of collage that was like this. It was more thorough compared to Euler's Theorem. My Teachers refused to even look at it because and I quote, "You are just a student, you could never come up with anything of value." or "There is nothing you could have come up with that someone else hasn't already found."
I sent you what I was able to work out through twitter. It has been over a decade since I came up with it and I just was remembering it off the top of my head so it may be not formatted correctly. I don't have any connections, so this is literally the best method I can think of to get any feedback on it. Yes this is just a shot in the dark... And now I am realizing that this is a old video and... nevermind... :(
Very cool. This reminded me of when I was first learning the times tables. I didn't enjoy memorizing them so I just memorized the 12 times table and convinced people that I new all the rest. Because I must if I can do 12x, right?
"Believe it or not, kids pick 69^5 a lot"
I believe it....
Here is the proof behind Euler's theorem for a^5 = 10m + a. I will use a proof by induction.
1.) Let's assume that a = 1, therefore, 1^5 = 10m + 1. 1 = 10m + 1. 0 = 10m, and therefore, m = 0. For m = 0, 1^5 = 10m + 1.
2.) Let's assume that k^5 = 10m + k. Where m is an element of the set of integers.
(k+1)^5 = k^5 + 5k^4 + 10k^3 + 10k^2 + 5k + 1.
(k+1)^5 = 10p + k + 1, where p is an element of the set of integers.
(k+1)^5 - k - 1 = 10p.
k^5 + 5k^4 + 10k^3 + 10k^2 + 4k = 10p
10m = k^5 - k
10p - 10m = k^5 + 5k^4 + 10k^3 + 10k^2 + 4k - k^5 + k = 5k^4 + 10k^3 + 10k^2 + 5k.
Therefore, 10p - 10m = 10(p-m). (p-m) is an element of the set of integers since the set of integers is closed by subtraction.
From Subproof Awesome, below, we know that 5k^4 +10k^3 +10k^2 + 5k is always divisible by 10 for no matter what integer k.
Therefore, a^5 = 10m + a
End of Proof
Subproof Awesome
We need to prove that 5k^4 + 10k^3 + 10k^2 + 5k is always divisible by 10 for all k in the set of integers.
Let's suppose that k = 1
5(1^4) + 10(1^3) + 10(1^2) + 5(1) = 5 + 10 + 10 + 5 = 30. 30/10 = 3, and 3 is an integer. Therefore, it is true for k = 1.
Let's suppose that for k = q is true, can we assume k = q+1 is true.
5q^4 + 10q^3 + 10q^2 + 5q = 10h where h is an integer.
5(q+1)^4 + 10(q+1)^3 +10(q+1)^2 + 5(q+1) = 5(q^4 + 4q^3+6q^2 + 4q + 1) + 10(q^3 + 3q^2 + 3q + 1) + 10(q^2 + 2q + 1) + 5(q+1) =
5q^4 + 20q^3 +30q^2 + 20q + 5
+ 10q^3 +30q^2 + 30q + 10
+10q^2 + 20q + 10
+ 5q + 5
_____________________________________
5q^4 + 30q^3 + 70q^2 + 75q + 30 = 10r, where r is an integer.
Subtract 5q^4 + 10q^3 + 10q^2 + 5q from 5q^4 + 30q^3 + 60q^2 + 75q + 30 and you get 10r-10h.
20q^3 + 50q^2 + 70q + 30 = 10(r-h)
10(2q^3+5q^2+7q+3) = 10(r-h).
As you can see, they are always divisible by 10.
Therefore, for all k integers, 5k^4 + 10k^3 + 10k^2 + 5k is divisible by 10.
END of Subproof Awesome
You used so many ks the ku klux klan is inviting you to their next lynching
+CopiedOriginality he didnt use a single K !
+Joseph Willes But how is that a proof by induction? If you prove that the base case works (the smallest example of it working or the first step that you take) then you prove that it will work for any variable that comes after. Usually for that step we let n equal a new variable k.
He is inducting on a in the main proof and then k in the subproof. There is no n.
This isnt Eulers theorem.
Eulers theorem is: a^phi (n) = 1 mod n
These guys never stop surprising me. Great job.
Dude this guy is legit, MORE OF HIM!!
Never take a pub bet against a Nottingham mathematician. :-)
Fun tip... @ 1:04 on the calculator, you don't have to keep typing *38 = .. *38 = ... *38= .... --------- You can just type *38 once then press the "=" sign 4 times in a row, it will automatically preform the last operation (that being *38)
I think he was trying to make sure people knew he was doing 38^5
Albert Renshaw or you could just swipe the screen to the right....you will get a scientific calculator
Or you could just write the result directly.
Love that stuff! Enjoyed it a ton.
This is one of the loveliest videos on the internet.
Euler's theorem can be easily proved:
The Little Fermat theorem says
a^p - a is divideable by p, IF p is a prime.
That means a^5 - a is divideable by 5.
If it's divideable by 5, then the last number must be 0 or 5.
If it ends with 5 then of course it's an odd number. If it ends with 0 then it's even. We just have to proof that it's even, so it ends in 0 every time.
The way we show this is by doing this (i don't know how you say it in english):
a^5 -a = a*(a^4 -1)
If a is an even number then of course a*(a^4 -1) is even.
If a is odd then a^4 is odd too, and a^4 -1 is even so our number is even again.
We proved that it's even and divideable by 5, so it means it ends with 0.
But if a^5 -a ends with 0, then a^5 ends with a.
Ooops, I mean a^5 ends with a 's last number
+Shri harsha Nayak Yeah, you're right sorry :/
Great number tricks, thanks for sharing.
Jjijijo
Awesome video! Keep uploading videos with Simon please!
ok , i will admit that i am more of a numberphile than i was before watching this video, this channel is not only for someone who is a numberphile to enjoy, it will slowly make you in to one, just give it some time . thanks a lot for everything :)
69 was a bit hard. But i got used to it.
please no
+COLW321 Gaming lennyface.jpg
( ͡° ͜ʖ ͡°).tiff
nope.avi
69 likes
"69 is a bit hard, but I got used to it." - Simon Pampena
That's a pretty neat trick. My usual math trick is to get someone to think of a number (while I think of the variable X), have them perform simple math operations (while I do the same to X), tell them to subtract their original number when I have some number plus X in my head, and then tell them what that number is. What's best is to ask what their favorite number is first and make it come out to that.
Example:
Pick a number, add 2, multiply by 3, subtract 3, divide by 3, subtract your original number: You're thinking of 1.
In my head:
X -> X+2 -> 3X+6 -> 3X+3 -> X+1 -> 1
no one in this world gets to business as quickly as Numberphile.. legit
I can seem like I'm smart now
JustAnotherSunny one thing I'd point out is that for the X0^5 stuff you can just know X ^5 and how many zeroes it would have at the end times 5 are added on. in fact this potentially allows you to if you pay attention to do any number to the power of 5 in theory except they overlap at times.
I wonder if he knows why kids choose 69^5...
likemynewname lol that's what I've been thinking
Pretty sure he does
He’s a mathematician, therefore he doesn’t know.
I’m a mathematician in the making so don’t take it too personally I’m just joking lol.
its because its used in lots of memes and stuff
They probably dont know the true meaning
The true meaning i-
Dude Im knows as the smart kid in my class and when I go back to school monday I'm gonna blow everyone's minds. You've done it again numberphile!
Nice vid as always
You can extend this trick to any odd power (my dad used to teach me how to do it to find cube roots). The basic idea is to remember 10³, 20³, 30³ and so on. And obviously know the last digit of any digit cubed (as the euler's theorem only works witha power of 5). It can also work for power 7, 9, and 11 (I have not checked other powers)
I didn't even know something called a fifth root existed.. :)
I gues you don t know the solution of X^5 + 5t*X^3 + 5t^2*X = -2q = 0 then.
This dude is just so... freakin... competent!!
Great job! You make me proud! 🤗
This is the best thing I have ever seen!
Damn it why couldn't all my math teachers in school be as enthusiastic as you?
Equis Igriegazeta teachers are enthusiastic when they don’t crash into unmotivated students... (as you?)
Awesome trick, thanks for sharing! ;)
Very nice vid and good explanation .
I love all these math tricks!
Love this channel. Really nice work. One note: you guys probably don't realize how a sharpie on brown paper sounds in a recording. To many people, it's worse than nails on a chalkboard.
never thought it was annoying to hear. then again.. i don't care too much about nails on a chalkboard either
Personal preference. I quite like it.
I actually quite enjoy the sharpie sound. It's not grating like a chalkboard.
I love this guy!
I get the feeling he is really smart, really really smart, and I always feel he could probably work it out in long hand if he wanted. Great video, thanks
I shall blow some minds now , Thanks Brady and Mr. Simon Pampena :D
This was extremely great!
This will forever be the nicest ending to a Numberphile video
I didn't know Russell Brand was a math genius!!
Prazkat Reviews He looks more like Matthew Santoro to me.
the first sword of bravos does not run
He really does not look all that much like Russell Brand.....Doesn't have enough of an aloof look about him for one.
He doesn't look enough like a slimy, bohemian socialist
Please give us more calculator unboxings. I need more. I need them!
I wish numberphile was around when I was at school. I was ok at maths, but I think if I saw the beauty in it I would have been far more interested.
That's a neat trick, but how likely am I ever to need to know the fifth root? It isn't like square roots or even cube roots, which come up all the time!
Haha, 69^5. Kids. XD
Awesome trick.
Bro you are greatest mathematician for me on youtube
Yay, new party trick!
...yes, my parties are frequented by drunk geeks, why do you ask?
No one is asking
Simple way to memorize the first digit.
10^5 is the same as 1^5 with 5 0s after
20^5 is the same as 2^5 with 5 0s after
and so on. So just learn your powers of 5
Kumartheffar that’s quite obvious, isn’t it?
Haha! It would've been awesome if the video ended at 1:39 right after he says "I'm a genius" And we were all like whaaaat? xD
The engineer joke at 4:53 made my day lol thanks 😊
I've seen this repeats with all (1+multiple of 4) powers like ^(1+4) or ^(1+8). The last digit stays the same.
To use a similar trick, you just have to learn the powers of the numbers from 0 to 9 (I guess is because 10 base numerical system.).
It does because a^5=10m+a, times this by a^4, and get a^9=10ma^4+a^5=10ma^4+10m+a, and same for a^8, etc
A slight variation of the trick allows for all 3+multiple of 4 powers.
This is really cool, can't really share because I don't want my friends to know about this :)
Happy Pi day!!!!!
Why does the number have to be in English?
Maybe he doesn't speak any other language...
Because in languages like German or Arabic, you don't say "sixty-eight", but "eight and sixty".
In German, for instance, it's "achtundsechzig" (8 and 60).
Hope that answers your question... albeit 4 years later.
Also was that a deer?
looked like it
this trick is badass, i'll definitely learn it!
Now this I could see trying to use in social situations. Very cool.
Whys there a deer in the back!!!?
I personally really hate the "root" notation. It just obscures the relationship with exponentiation. Is it really that much harder to say to the 1/5 power instead of 5th root?
yes, however my advice is: deal with it. that's the least of problems a mathematician could have.
also, is anyone stopping you from using the power notation and not using the root-notation at all?
That's really only a problem when kids first learn about them (like 2pi vs tau) and with little practice it becomes hard to tell if it was ever a problem to begin with. If you really want you could mess with people by saying "the 1/2th root of X" for X^2.
how much harder is it to multiply by a fraction to divide, or add to a negative number to subtract?
i love watching this man talk about maths.
I really love when you post this videos with captions. I'm brasilian and i really don't understand much things. The math is ok, but i lost all jokes :/
do a video on 1,000,000 factorial
The only issue is giving him a non-perfect fifth root, such as taking the fifth root of a random number like 766445.
That's the trick, he said think of any two digit number. This implies it's an integer between 10 and 99. Then he told that person to multiply it by itself 5 times and tell him the result.
They didn't start by giving him a large number and asking for it's fifth root, that would likely not be an integer result.
“That’s STILL a big ask, to memorize all that” LOL - I too, was here hoping that the trick were a lot easier than this- 😅
Really cool!
5:50 I wonder why the children say 69 :3 koff koff
***** I have no idea what you're trying to say.
Samurai Nakruf Because they are immature?
WarpRulez no, to trick him. :D
***** 69, 9 is just 6 upside down so its neat and easy to remember pattern.
GameDogLeader21 Sure, but that's not the reason the children find it amusing to suggest it and get excited about it
does this work in other bases other than base 10 such as base 12? I'm too lazy to figure it out myself.
wow pretty cool! I like this trick
Awesome, thanks
Pause at 1:05. Scary.
phi(10) = phi(2)*phi(5) = (2-1)(5-1) = 4
awesome! thanks for sharing :)
You are my hero
well, memoization may work for these small numbers, but what to do, if I am handling sextillions ??
0:37 O-oooooooooo AAAAE-A-A-I-A-U-
JO-oooooooooooo AAE-O-A-A-U-U-A-
E-eee-ee-eee AAAAE-A-E-I-E-A-
JO-ooo-oo-oo-oo EEEEO-A-AAA-AAAA
…What?
NoriMori Brain power!
Osu! somebody? Please?
+Nano poison What?
Oooohhhh ahhhhhh Oooohhhh ahhhhhh I love Tzuyu
That was a great trick.
this guy is my favorite
1 min in when he is on the calculator; Simon goes into "Gollum mode" :) hahahahahaha
I failed Algebra 2...what am I doing here
Cuz math is beautiful
Learning.
Cool stuff :) Can be extended to quite a few powers. (Prime powers). Neat use of the euler's theorem.
Thanks For The Vid
hey Braidy ask your proffesors about spheres. more precisely about
1. turning sphere inside out
2. makeing 2 spheres (or actualy any number of spheres) from one sphere (you can cut a sphere into very small puzzle pieces and then when you put these pieces back together you can do so in such a way that you can make two or more spheres)
Unpronouncable talk shite pal
#2 is a Vsauce video
@@zashtozabogaepisode on Banach Tarski paradox