Square Root in 3 seconds - Crazy Math Trick

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  • Опубліковано 24 гру 2024

КОМЕНТАРІ • 122

  • @greninjamariokartpokemonfan
    @greninjamariokartpokemonfan Місяць тому +34

    58²=3,364
    (a+b)²=a²+2ab+b²
    (50+8)(50+8)
    2,500+2(400)+64
    2,500+800+64
    3,300+64=3,364
    (a-b)²=a²-2ab+b²
    (60-2)(60-2)
    3,600-2(120)+4
    3,600-240+4
    3,360+4=3,364

    • @xdreamwalked
      @xdreamwalked Місяць тому +4

      50^2 = 2500
      8^2 = 64
      25+8=33
      3364
      😅

    • @dhruvsantra9027
      @dhruvsantra9027 Місяць тому +2

      Why 25+8??

    • @xdreamwalked
      @xdreamwalked Місяць тому +1

      @@dhruvsantra9027 because 58 is 8 away from 50. this trick revolves around 50. 42^2 for example would be 8 away from 50 and 8^2 is 64, 25-8 = 17 so 1764

  • @SnowyPlayer
    @SnowyPlayer Місяць тому +140

    Since this trick only applies to perfect squares, could you tell me how do I find out whether the number is a perfect square or not without the need to taking the square root of it, please?

    • @brain_station_videos
      @brain_station_videos  Місяць тому +38

      Right now, I know one method for that called binomial expansion, but I’ll make a video if I find a simpler method.

    • @scmtuk3662
      @scmtuk3662 Місяць тому +29

      Prime factorization.
      If you can express the number as a product of prime factors in which there is exactly an even amount of each prime factor, or, in other words, when expressed in exponentiation form, all the exponents are even, then the number is a perfect square.
      For example, the prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5 or 2² x 3² x 5².
      Since all the powers are even, then the number 900 is a perfect square. This is because 2² x 3² x 5² = (2 x 3 x 5)² = 30².
      If you get the prime factorization of 500, that would be 2 x 2 x 5 x 5 x 5.
      This is then written as 2² x 5³.
      Since there is an odd number of 5s being multiplied, 500 isn't a perfect square.
      Infact, if you take the square root of 2² x 5³, you are left with √(2² x 5³) =
      √(2² x 5² x 5)
      √2² x √5² x √5 =
      2 x 5 x √5 =
      10 x √5 =
      10√5.
      In short, find the prime factorization of the number. If you can group all the factors into pairs, without any left over, then the number is a square.
      In fact, if you can group the prime factors of a number, in to groups of "n", then the number is a perfect nth power.
      For example, if you take 1728, and find the prime factors, you will get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.
      If we group these into pairs, we will get (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x 3.
      Since there is an extra '3' that isn't part of a pair, 1728 is _not_ a perfect square.
      _However_ we can group these into 3s:
      (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3).
      This means that 1728 is a perfect cube (power of 3).
      In this case, if you take one number from each group, and multiply them, that is your cube root (i.e. 2 x 2 x 3 = 12).

    • @Данил-з7о6з
      @Данил-з7о6з Місяць тому +2

      You can just check your answer by squaring it

    • @memes_3575
      @memes_3575 Місяць тому +1

      Ex: sqrt of 926
      You just need to know some numbers like 10×10=100, 20×20=400, 30×30=900 and so on
      You get the the number 30 forward and multiple then by thenselfs
      30x30=900
      31x31=961
      So its about 30,5 or less,this part you calculate by hand to be easier
      I hope yall get it,cuz it helps a lot 😅

    • @RustyMadd
      @RustyMadd Місяць тому +1

      Numbers ending in 2,3,7, or 8 are not perfect squares, Numbers ending with 0,1,4,5,6, or 9 can be, but are not necessarily.

  • @denysmace3874
    @denysmace3874 Місяць тому +57

    It's a nice trick, but one small quibble. You started off saying you only need to learn the squares of 0 through 9, and you end by casually throwing in the square of 12.

    • @Bruh4502
      @Bruh4502 Місяць тому +6

      Well finding the square of 12 is definetly better than finding the square root of 15876 (if it was possible without using this method) so i don't think its a big deal to complain about it

    • @denysmace3874
      @denysmace3874 Місяць тому +8

      ​@@Bruh4502hi. Well, I wasn't actually complaining. I think it's a nice video, and I like nifty maths tricks like this.
      You have to admit, though, that he did start off saying you only have to know squares up to 81, but within a few minutes he'd moved to, you all know the square of 12 is 144. My comment was really meant in a light-hearted way.

    • @brain_station_videos
      @brain_station_videos  Місяць тому +8

      Sry...my bad

  • @scmtuk3662
    @scmtuk3662 Місяць тому +12

    There is no way most people would be able to pick the number(s) who's square ends with the same digit as the square we're trying to find the root of, then remove the last two digits of the answer, then find the number who's square is less than the remaining part of the number without the last two digits, then multiply that number by the next number, then choose the greater of the two possible last digits, if the original number is greater than the number we got by multiplying the number who's square is less than the part of the number we got by removing the last two digits..... in 3 seconds.
    Also, if the difficulty of a task is unrelated to the time it takes to do a task, then another way of finding the square root of a number, is the use of prime factorization.
    For example, for 3364, we will find the prime factorization:
    3364 | 2
    1682 | 2
    841 | 29
    29 | 29
    1
    Now we simply write the product of the numbers in the second column, like so:
    2 x 2 x 29 x 29
    To simplify this, we can then rewrite this expression in the form of exponents:
    2² x 29²
    Then we can simply take the square root of this product, to find the answer is 2 x 29 = 58.

    • @yoro.jojjowi
      @yoro.jojjowi Місяць тому +1

      Way better trick but more complicated, I'm only In 6th grade and if i was in 8th grade I can do it, either way, thanks

    • @soumyanandan1567
      @soumyanandan1567 Місяць тому

      ​@@yoro.jojjowi damn you better start studying now brother if you want iit

    • @Uninspiredz
      @Uninspiredz Місяць тому

      Hey thanks for this
      But how we remove the square roots in the last step?
      -does 58 have to get simplified
      -does 58 have a square root?
      -what do we do with 58 then?

    • @scmtuk3662
      @scmtuk3662 Місяць тому

      @@Uninspiredz Um.... you are aware that 58 _IS_ the square root, right?
      If you're asked to find the square root of 16, and you get 4, what do you do with the 4? Nothing. That's the answer. You do realize how ..... life works, right? Did you find out that 1 + 1 = 2, then ask "what do you do with the 2?"

    • @Uninspiredz
      @Uninspiredz Місяць тому

      @@scmtuk3662 bruh I forgot how it worked for a sec.
      I just asked a Question, calm down

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs Місяць тому +135

    Sqrt[3364]=58

    • @lukatolstov5598
      @lukatolstov5598 Місяць тому +6

      Please no spoilers

    • @MarkGerald2011
      @MarkGerald2011 Місяць тому +21

      ​@@lukatolstov5598Then why are you reading the comment section before the video starts?

    • @GomVorder78439
      @GomVorder78439 Місяць тому +19

      ​@@MarkGerald2011probably because it showed up when clicking on the video.

    • @MarkGerald2011
      @MarkGerald2011 Місяць тому +8

      @@GomVorder78439 probably he's using his phone not pc or smth

    • @FnaftheUltimateking2
      @FnaftheUltimateking2 Місяць тому

      ​@@lukatolstov5598it's not a spoiler because he doesn't solve this in the video

  • @Sweetcow24
    @Sweetcow24 4 дні тому +1

    Tysm this helps me save so much time in solving problems

  • @Ohio_Renz
    @Ohio_Renz 9 днів тому

    Square root of 3364 is 58. Because find the square of 4. Choose either 2 or 8. Cancel 2 digits. Square Root of 33 is Irriational Number. But remove the decimals. Then the answer is 58

  • @aaditmordani
    @aaditmordani Місяць тому +6

    @Brain Station how did you get 12 x 13 in 4:15

    • @sopiestbanana2181
      @sopiestbanana2181 Місяць тому +3

      Multiply the number by the one after it

    • @tommytress77
      @tommytress77 Місяць тому +3

      What is 12 + 1? 13 right? Here we are supposed to multiply the first number by it's successor, not the 2nd or 3rd number

    • @Fire-b4
      @Fire-b4 Місяць тому +1

      ​@@tommytress77 why is Tommy here solving math problems 💀

    • @tommytress77
      @tommytress77 Місяць тому +1

      @@Fire-b4 math good
      🙂👍

  • @Steven-v6l
    @Steven-v6l Місяць тому +11

    misleading ... the trick allows you to quickly recognize a perfect square. it would take a normal person more like 30 seconds to apply the trick

  • @Evan-z6t
    @Evan-z6t 11 днів тому +1

    Can you make more videos that teaches tricks like this

  • @Sħmabdul
    @Sħmabdul 28 днів тому +2

    this is helpful you are a good youtuber

  • @thinkglobal-9923
    @thinkglobal-9923 6 днів тому

    Thanks.You made my life easier

  • @jeffw1267
    @jeffw1267 Місяць тому +2

    Another quick way to find the correct answer between two choices is to cast out nines. For example, if the square root of 729 is either 23 or 27, we can first check 23 as a root by adding the digits together. 2+3 is 5, which gives us a remainder of 5. 23x23 gives us two remainders of 5, and we multiply them to get 25. 2+5=7. The nines remainder of 729 must also be 7, or we have the wrong root.
    7+2+9=18, 1+8=9, and we can cast out the 9, giving us a remainder of zero. Seven does not equal zero, so 23 is not the correct root, and that leaves 27 as the only possible answer.

  • @Lucky-d6v5u
    @Lucky-d6v5u Місяць тому +9

    Amazing trick bro 🔥

  • @amishgamerx
    @amishgamerx 9 днів тому +1

    What about numbers not having perfect square

  • @SnapShorts66
    @SnapShorts66 Місяць тому +25

    this would 100% take longer than 3 seconds for starters

  • @kennethkan3252
    @kennethkan3252 Місяць тому

    3364=4mod8
    =(2mod8)x(2mod8)
    33>5^2
    64=8×8=4mod8
    58=2mod8

  • @rmadhavan7308
    @rmadhavan7308 Місяць тому +21

    can you give some extra problems after each vid?? it would help al lot

    • @brain_station_videos
      @brain_station_videos  Місяць тому +5

      Sure

    • @luno1884
      @luno1884 22 дні тому +1

      Broo got to chatgpt and say
      Hey give me some 4 digit numbers of perfect square done

  • @davidkelly3751
    @davidkelly3751 29 днів тому

    start with 60^2 = 3600 then minus 60, 59, 59 58 to get to 3364. So answer is 58

  • @strikerbravo303
    @strikerbravo303 12 днів тому

    2:09 can we get 4^2 or 6^2 instead?

  • @alphaadarsh88
    @alphaadarsh88 28 днів тому +3

    3:46 in this section why didn't you multiple 5×4

    • @rimimondal6806
      @rimimondal6806 19 днів тому

      The rule is to multiply the number to its next number. n*(n+1)

  • @_Paps
    @_Paps Місяць тому +1

    whats the thing/rule that allows this trick to actually work?

  • @munna_says
    @munna_says 12 днів тому +1

    How could crack like jee exams

  • @DrMattFen
    @DrMattFen Місяць тому +4

    If I only had 3 to 5 seconds i would have guessed wrong.. Might be easier to just "simply" _memorise_ them all..

  • @spaceguy20_12
    @spaceguy20_12 Місяць тому +11

    ask a German if they know what the square root of 81 is, if they know, you get the correct answer, if they don’t know, you also get the correct answer

  • @Maths_Wonderland
    @Maths_Wonderland 24 дні тому +1

    Which app do you use to edit your videos?

  • @NOBODY-z8j8y
    @NOBODY-z8j8y Місяць тому +1

    So good, keep going 👏 💪

  • @aryan_yashdeep
    @aryan_yashdeep 16 днів тому

    3364:- 2/8 and 5 then 58

  • @bosensworlds6089
    @bosensworlds6089 Місяць тому

    How do we pick, choose the first number or the second number?

  • @Talking__Ben
    @Talking__Ben Місяць тому +2

    I'll just keep using the sqrt function on my calculator

  • @Xter-Sells
    @Xter-Sells Місяць тому +1

    appreciated 🔥

  • @Odysseus_pneumomia
    @Odysseus_pneumomia Місяць тому +2

    What If It ends in 2,3,7 or 8?
    Just go for the closer one? Higher one or lower one?

    • @dinosatay
      @dinosatay Місяць тому

      then the number isn't a perfect square, and the root isn't a neat rounded number
      (this method can't be used for numbers which aren't perfect squares to begin with)

    • @Odysseus_pneumomia
      @Odysseus_pneumomia Місяць тому +1

      @dinosatay thanks bro

  • @theJoeDeckerShow
    @theJoeDeckerShow 6 днів тому +1

    Super thanks

  • @TheBldCube
    @TheBldCube Місяць тому

    Sqrt[9]

  • @Bluebird_YT
    @Bluebird_YT Місяць тому +2

    Also works for cuberoot

  • @Never_miss_613
    @Never_miss_613 6 днів тому

    Bro what is the name of this trick😢

  • @asaventurasdejosh
    @asaventurasdejosh Місяць тому

    sqrt(3364) = 58.

  • @darksentinel3620
    @darksentinel3620 Місяць тому

    does this work for all perfect squares?

  • @Rokoasusmous
    @Rokoasusmous Місяць тому

    That's because Jesse is at home, you're not. Time and feel again?

  • @harryrapha4398
    @harryrapha4398 28 днів тому

    nice trick broo

  • @classicoianomusic
    @classicoianomusic 12 днів тому

    and if the last number is 7 or 2?

    • @CrYou575
      @CrYou575 5 днів тому

      Then it can't be a perfect square.

  • @SUPERNOVAx2bBlu
    @SUPERNOVAx2bBlu Місяць тому +1

    4:30 58

  • @thecricketmerchant
    @thecricketmerchant 25 днів тому

    Fun fact
    81x196=15876

  • @JarppaGuru
    @JarppaGuru Місяць тому

    1:41 so you saying 1525 1425 1325 1225 1125 1025 925 like you said answer would be 35 and how know square will be integer, bcoz non other those are LOL and that 5 meaningless but sure it wil bee 3 but that 5 fails. ou cant know did you make it correct. so how know?

  • @SunriseChannelS
    @SunriseChannelS 4 дні тому +1

    58❤❤

  • @fritsvanzanten3573
    @fritsvanzanten3573 Місяць тому

    Nice. But I'm afraid only useful in quizzes.

  • @AndrewBlucher
    @AndrewBlucher Місяць тому

    Trick without an explanation is just a trick

  • @sixbal2886
    @sixbal2886 Місяць тому

    lol i calculated the first one in 5 seconds before watching the video

  • @ZannatunNaim-gz8zn
    @ZannatunNaim-gz8zn 25 днів тому

    I may do this ib my calculator 😂

  • @redeyedragon5389
    @redeyedragon5389 День тому

    wait how did bro get 27 for the first one isn't it 35?

  • @ElijahsAnimationChannel
    @ElijahsAnimationChannel Місяць тому +3

    Root😊

  • @scottnorin
    @scottnorin Місяць тому

    I can just get a calculator and get the answer in less time than this video

    • @AlexDiverxu
      @AlexDiverxu Місяць тому

      waiting for you to get a calculator and press the button to get the answer? too slow,
      two dights sq, must start with 5 and end with 8, END

  • @John-x1h1j
    @John-x1h1j Місяць тому

    didn't work for 998,001, at least not for me

  • @SteveM45
    @SteveM45 7 днів тому

    With calculator its faster

  • @LovelyBrain2
    @LovelyBrain2 Місяць тому

    58

  • @Apeiron242
    @Apeiron242 Місяць тому

    Thumbs down for using a robot voice.

  • @T̨̐P̵̹̰̱G̵̈̃̑-hi
    @T̨̐P̵̹̰̱G̵̈̃̑-hi Місяць тому

    Skibidi

  • @christianquingcong227
    @christianquingcong227 Місяць тому

    John 14:6
    New King James Version
    6 Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.

  • @Arkeedeos
    @Arkeedeos Місяць тому

    Noice

  • @steven2809
    @steven2809 25 днів тому

    What a waste of time.....

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs Місяць тому +4

    Sqrt[729]=27

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs Місяць тому +3

    Sqrt[1225]=35

  • @kam-cz6ex
    @kam-cz6ex 23 дні тому

    4:30 58

  • @karthickrahulg4259
    @karthickrahulg4259 Місяць тому

    58

  • @周小钧
    @周小钧 Місяць тому

    58

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs Місяць тому +4

    Sqrt[15876]=126

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs Місяць тому +4

    Sqrt[2916]=54

  • @_k_girl_781_
    @_k_girl_781_ 11 днів тому

    58

  • @Mainakmotivation07
    @Mainakmotivation07 10 днів тому

    58

  • @IndrakantMandal-g3l
    @IndrakantMandal-g3l 7 днів тому

    58