BELIEVE IN ALGEBRA, NOT CALCULATOR

everybody knows one plus one is equal to two  but I know two is the same as one plus one okay okay that's do some math for fun here work on  compute the square root of 100 times banjo and 100   2 times 9 3 and then plus 1 everything sings  out the square root of course we will not be   using a calculator because otherwise where's  the fun right and as always please pause the   video and try this first okay hopefully get to  have a chance to try it and let me tell you guys   that the answer to this right here is 25 and then  15 and then 0 1 like this yeah of course I didn't   do this in my head I did this beforehand and I  memorize the answer and I just put on the answer   for you guys by the way I'll show you guys how  to do this right here and here's a deal whenever   the question is asking you to compute some  crazy-looking expression without a calculator   usually don't use a calculator use algebra for  it of course if you can use a calculator it's   the easiest but you're using a calculator why  are you watching my video for this right so we   all make the observation so we can see how to  change this into an algebra equation and as we   are not the easiest way to compute square roots  that we hope the insights just a perfect square   that's the best one right so maybe the insides  actually a perfect square you will see so here   we go let me write this down here for you guys we  will make some observations first of all notice   that we do have a nice pattern right here and  if you call the first number to be X and the   next number will be X plus 1 and then we have  X plus 2 and this number will be X plus 3 and   don't forget a plus 1 right there as well and now  don't multiply these out in comparators entirely   because that would be just as bad as doing this by  hand in the first place right huh let's see first   of all though you might be wondering could we let  this be X so this is X minus 1 and this is X plus   1 and X plus 2 word up easier you can give you a  try I will continue from here right so let's see well seriously we are not going to multiply  everything out but if you look at because you have   done so ultra so many times if you multiply this  and that you can sound pretty nice is pressure   and let me write that down right before you guys  again just this in that we will end up X square   plus 3 X plus 2 and this is very nice because if  you multiply out the rest which is this X with the   X plus 3 right here they are going to be very  similar because you are going to get X square   plus 3 and notice this right here has the plus  2 this right here just the first two terms right   here so they are pretty similar to each other and  don't forget the plus one right here yet and now   here's the deal everybody knows one plus one is  equal to two by no - it's a same s 1 plus 1 well   I feel like a genius already check this out look  at this - I'm going to look at the 2 s 1 plus 1   and by doing so I can do kit insight as four terms  this this this and that right and I have this in   front so I would distribute this carefully first  of all this is how we will do it I will take this   right here and distributed with the first three  terms so we will end up x squared plus 3x and then   the first three terms himself this parenthesis we  get x squared plus 3x plus one like this and then   we'll take this times the one which is just that  by itself right so we can just write down plus x   squared plus 3x times 1 which is doesn't matter  and then thankfully we have another plus one   right here that's very nice and you'll see that  this is technically our first term because we're   these times that and then you have this right here  this is the same as that so we can actually factor   this and that out very nice so here's the deal  I will factor this out we get x squared plus 3x   plus 1 and the left over is this right here which  is x squared plus 3x and just like you out about   teacher will tell you don't forget it's like this  and you have the one right here so you have to put   down the plus one like this very nice as you all  know the best friend of black pen is of course   repent this and that they're best friends why  because together they produce a perfect square   so we get x squared plus 3x plus 1 to the second  power this is very nice and now the original   expression is just going to be you can put this  inside and of course this end our can so very nice   and you just get x squared plus 3x plus 1 and your  profound doing there so you get parentheses 500   square plus 3 times 500 and then plus one master  see guess don't you guys just love the Google   algebra days right anyway it multiplied everything  you get that number so this is it maybe you guys   noticed this is very similar to the answer that we  got found at video right few days ago because can   leave a comment down below let me know what the  video is all about right which video am I talking   about ok one of my previous videos some of you  guys asked me about the divisibility rule so I'm   going to show you guys more about this right here  on boolean to work first off I want to thank them   for spotting this video and also wanted to show  you guys about their new feature called daily   challenges and they happen to have this question  for today what's the remainder when you have 1 1   1 1 1 1 divided by 3 hmm I think the answer is 0  yeah I'm going to submit that and I got it correct   of course because I know the secret and if you  guys want to know more about a secret of course   you have to go check out the students and maybe  I'll do the video right here for you guys as well   but the interesting thing is that I think many  of you guys know about the defensibility rule   for numbers three but how about the other ones  if you would like to know more you guys can't go   check it out this right here right for the creases  so if you have about like five ten minutes per   day you can just pull this out and then you can  continue your learning right while you are just   enjoying your coffee and all that and I think  it's really really cool and maybe - another one   for you guys to just show off this right here  it's actually not divisible by three and I got   the correct of course and they also offer a  lot of interesting courses so if you want to   sign up for your annual premium subscription if  you guys use the link brilliant artwork slash   black pin repent because this way you guys can  get 20% off discount and you think it ssj4 all   of their courses another question for you guys is  that is this a prime number just think about as   well very cool question anyway probably gets all  like this video if you do please give me a like   if you're new to my channel be sure to subscribe  thank you guys so much and as always that's it

Channel: blackpenredpen

Views: 1,192,981

Keywords: beleive in algebra, The secret is to factor x(x+1)(x+2)(x+3)+1, math competition problem, blackpenredpen, math for fun, square root of a big number, is this prime, brilliant.org, challenging algebra problem

Id: P3ifP2GpMAo

Length: 7min 55sec (475 seconds)

Published: Fri Apr 05 2019