This man a living legend he’s helped so many people, Teachers aim to be you. I cannot thank you enough I’m taking high school dash one and this is beyond helpful. I honestly wish you were a teacher at my school.//Many thanks keep it up👍🏽
@Vaasu Gupta Maybe learn vedic maths or abacus, I have learnt abacus, and I did it in seconds. but if you don't have much time or something and you are trying for olympiads or tests, learn vedic maths
im only 13 and my pop is trying to get me ahead sometimes i cant understands the way he teaches me but you gave me a clear explanation thanks for putting in your time and effort
LEARN THIS LEARN THIS LEARN THIS!!!! Your dad is a good man getting you to be ahead of the curve! Don't ever assume you won't need these things because until you choose your career path after college you don't know what your boss may need you to know!
Josh Ciruli similar situation I’m twelve and my mom wants me to learn this stuff because I’m learning Algebra next semester. But she doesn’t teach me, she just gave me a workbook 😂
oh my god thank you so much we're doing that in school right now and i missed a few days and no one bothered to explain it to me so thank you for making this!!
@@shirosejiokami4168Yes you are right bro, now I am in this situation. Maybe now you have an office job and forget about this bad system that excludes honesty.😂
I have learnt all of my math from you Sal Khan. You are my true teacher. You have helped me rise in math to be one of the top mathematicians in my school. Thank you so much for your help.❤❤❤
Thank you so much, especially for giving actual reasons for doing this. The rocket science example flicked a switch in my head. When I was in high school no teacher could ever give a practical reason for anything other than "It's on the test," so I thought it was kind of stupid. Now that I am going back to college (after seven years) I love math, and this makes sense to me. Standards are crucial for collaboration: brilliant.
How do you do that man, literally had my teacher explain this, and I did not get it. Having you explain it once and I completely understand. It's crazy. Thank you so much.
When stating the difference is squares, it gets a bit confusing but a binomial fraction that has a irrational denominator we use this formula to factor the difference using square to make it rational. Just for the denominator? Math is so much fun.
سبحان الله وبحمده سبحان الله العظيم استغفر الله العظيم الذي لا إله إلا هو الحي القيوم و أتوب إليه سبحان الله وبحمده عدد خلقه ورضا نفسه وزنة عرشه ومداد كلماته اللهم صَلِّ وسَلّمْ عَلَى نَبِيْنَا مُحَمد ﷺ
LOL, we were learning this in school, and I was like fuck it.... might as well go on UA-cam on my phone and learn everything in 10 mins on khanacademy... thanks man this really helps
Thank you so much! I was googling how to divide surds when I glimpsed at the title of this video. I did n't even need to watch the video...(whisper) the title says it all.
@@utea5548 This is because some surds are best defined just as they are, in terms of accuracy. As some surds when simplified, gives us recurring decimals, which would be inconvenient and inaccurate to write as decimals, which is why it is better to leave them as surds. Mathematicians are lazy, you know.
Though technically sqrt(5) times 2 would be equal to sqrt(5) times sqrt(4), which would equal sqrt(5 times 4) or sqrt(20), and from there you can rationalize without the conjugate.
"why do we care, why do we have to rationalize the denominator?" because it's going to be on my test :(
Angela Rose 😂😭
Angela Rose It’s for limits and continuity in calculus
Supah X I’m doing this in integral calculus I wish I learned earlier lol
because i need bloody marks ,
So true 😆
This man a living legend he’s helped so many people, Teachers aim to be you. I cannot thank you enough I’m taking high school dash one and this is beyond helpful. I honestly wish you were a teacher at my school.//Many thanks keep it up👍🏽
ikr
Agreed
@Vaasu Gupta Maybe learn vedic maths or abacus, I have learnt abacus, and I did it in seconds. but if you don't have much time or something and you are trying for olympiads or tests, learn vedic maths
@@mariomontero7721 bro is brainwashed
@@apexspirit3793 huh?
im only 13 and my pop is trying to get me ahead sometimes i cant understands the way he teaches me but you gave me a clear explanation thanks for putting in your time and effort
Josh Ciruli ur so lucky to have a dad like that
LEARN THIS LEARN THIS LEARN THIS!!!! Your dad is a good man getting you to be ahead of the curve! Don't ever assume you won't need these things because until you choose your career path after college you don't know what your boss may need you to know!
Your dad is a good man.
Josh Ciruli similar situation
I’m twelve and my mom wants me to learn this stuff because I’m learning Algebra next semester. But she doesn’t teach me, she just gave me a workbook 😂
Gosh i cant understand this in class and we had an assignment soooo,that is why i went here
when i was still in highschool, i thought this is gonna be useless..
now im in college, ahahahahahaha back to basics
Thanks you good sir
Chris Hernani Same
this is basic???
Yes, very basic when it comes to Algebra 2 or higher levels of math.
Well if you are in Film College, it’s basically useless
HAHAHHAA TRUE
oh my god thank you so much we're doing that in school right now and i missed a few days and no one bothered to explain it to me so thank you for making this!!
cant imagin u were 9 years younger typing this.prob in high school
@@hi_its_me_again6128 lmaoooo you took me back
You sir, are one of the best teachers I have ever learnt from, Thank You.
I just don't understand why rationalization is done.
I dont see why there are grades, and if below 70 u get held back...why school
@@shirosejiokami4168 You want to be stupid all your life?
@@shirosejiokami4168Yes you are right bro, now I am in this situation. Maybe now you have an office job and forget about this bad system that excludes honesty.😂
Yep, pretty sure gonna fail my exams now
Did u fail??
😔🙌so am I
@@cacalightx how would she remember now?
🤣🤣🤣🤣🤣🤣
😂😂😂
I have learnt all of my math from you Sal Khan. You are my true teacher. You have helped me rise in math to be one of the top mathematicians in my school. Thank you so much for your help.❤❤❤
Lamo now that we are doing online schooling do to the quarantine, my teacher just leaves a bunch of links to your videos to teach us
Eric macisaac yep and him I still don’t understand
that was creepy
Again perfect timing!!!!
We are doing it class now!
I am so happy!
I guess you graduated hahaha
@@genox633 you just casually replied to a comment after 12 years lol
Bro must have turned into successful person now
boo
Well I wish you were my teacher. My teacher doesn’t teach, we have to teach ourselves and she expects us to know how to do everything
that sums up my maths teacher perfectly (no pun intended)
Thank you sooooo much. I can't tell you how many time your videos and great explanation skills have saved me!
Thank you so much, especially for giving actual reasons for doing this. The rocket science example flicked a switch in my head. When I was in high school no teacher could ever give a practical reason for anything other than "It's on the test," so I thought it was kind of stupid. Now that I am going back to college (after seven years) I love math, and this makes sense to me. Standards are crucial for collaboration: brilliant.
the best tutorial i have seen in the world of youtube.
thank you so much im taking my maths GCSE exam in november and this is the main topic i was struggling on, but not any more thanks to this video :)
Thank you sir. In 2 days there is my math exam and still I didn't know how to ratlionize until I saw your video. Thank you once again.
Posted 11 years ago and still gold! :)
How do you do that man, literally had my teacher explain this, and I did not get it. Having you explain it once and I completely understand. It's crazy. Thank you so much.
chemical engineering student and this helped me 13 years later
I'm in my senior finals, I can't remember the last time we had done this in school, but thanks you sir, I'm gonna be okay
I hope you enjoy an easy life because you make our lives easy
This is amazing. I wish you were my math teacher!
this would have prevented a fist fight the last time my friend and I built a rocket
Teaching level:100
Sound level:50
well this was 11 years ago and when you commented it was 8 years old, so the it is understnadable.
I'm so done! This makes no sense in my classroom
Math (in primary) - Piece of cake :)
Math (in secondary) - No comments :(
Math in uni: "Can we get some numbers? Pretty please?"
@@JackBlack-qn7us no :>
I LOVE YOU KHAN ACADEMY!!!
ikr
Thanks sir you helped me a lot...
❤❤❤😍😍😍
Now I m very familiar with rationalising..
INFINITE THANKSSS 🙏🙇
It aided me a lot for converting a pair fraction of variables into a like fraction to add up ... (qu. Formula)
Thkx u khan acedmy
You just solved my home work for me :)
Thanks :)
i subbed to him because i needed help in math. this guy is the best teacher ever.
wow sir i got something here thank u
When stating the difference is squares, it gets a bit confusing but a binomial fraction that has a irrational denominator we use this formula to factor the difference using square to make it rational. Just for the denominator? Math is so much fun.
6:58 why did it become - 24 MINUS 12 root 5??? it was just plus a while back
Because it's math!
Jk it's because the -1 is the denominator to both of them and when they split up they both become negative
You have a very helpful collection on videos here.
Brilliant Khan sir!
Thanks a lot Khan Academy. I had a test tomorrow, and this video helped a lot!
Yeah But Still
what do u mean
Hey shaaz im coming this week
forever permanent
Forever permanent
I have an final exam to final grade 09
The lesson who stay to me is
RASTIONALIZE
Khan Academy is truly the savior of all students.
At 7:02, why did sal put a negative sign in front of the 24? Isn't it positive 24..?
really Aditya Guin you dont know this
no i really dont.
ok its fine Aditya Guin , it is preety easy,i can explain this to you in math
well now i now
ok
Love from india
Thank for this s video
سبحان الله وبحمده سبحان الله العظيم
استغفر الله العظيم الذي لا إله إلا هو الحي القيوم و أتوب إليه
سبحان الله وبحمده عدد خلقه ورضا نفسه وزنة عرشه ومداد كلماته
اللهم صَلِّ وسَلّمْ عَلَى نَبِيْنَا مُحَمد ﷺ
thankyou very much sir love from Pakistan
I think I’ve watched this video at least 4 other times during high school. Now here I am college trig needing help again
Awesome Bro i am learning this at my school
thank you this was a great help on explaining what I was doing wrong
so glad to have this, currently studying for a college exam tmr
thanks for the great videos Khan Academy - and your new windows 8 app is great contains all videos, recommend all of you go and get it - its FREE!
Heard it guys? We rationalize the denominator for esthetics ಥ‿ಥ
Teacher explain very well!
daug this vid was made when i was born yet its still so helpfull wow
thank you smmmm I finally understand why we use the conjugates
The question I always got wrong on the test. Excellent now I can ace my final :D thank you!
Have you graduated?😂
Thank you sir...😊😊 ❤ from India,kerala
Sir l swear u r the best
From KSA🔥
At 3:50, wouldn’t that work? Because the square roots of 5 would cancel out, leaving 12/-3 = -4
hey man you are the latest comment, can I ask you a favor?
4/(√2 +1)^2
can I make it like === 4/ 2^2 +1^2 ?
@@batman1542 the square root of 2 to the power of 2 would cancel out, and 1 to the power of 2 is 1, leaving you with 4/2, or 1/2
I like how everyone here is doing this in 9th grade while im over here doing this in 10th grade because my country's education is so behind
7th :)
at 5:30 i think it was supposed to be +5 because sqrt-5^2 is -5 and -(-5)=+5
Great lesson thanks for your effort
If I’m not wrong outside of the US it’s called Conjugate Surds.
Seems easier. Look it up if some of you are still struggling
How about some other irrationals like pi?
Thanks for this nice explanation, I can rationalize now, but I still hate math.
It's 10 years from now, my question is in 7:02 did you distribute the - to +12sqrt(15), that's why it became -12sqrt(15)?
Sal i simply cannot thank you enough for your existence
Thank you khan academy. You saved my life more than once. I love you
So helpful
I ignored this in highschool now I'm doing Computer Science and I need this for calculus.
LOL, we were learning this in school, and I was like fuck it.... might as well go on UA-cam on my phone and learn everything in 10 mins on khanacademy... thanks man this really helps
LOL
What if you have a cube root squared?
Cube root isn't squared cube root is to multiply itself by 3 in essence if you wanna cancel a cube root you do that by Cubing it
@@realmoe6410 that was not totally confusing at all!!!!
You rock .
I want a teacher like you for myself
Dear lord thx a lot Sal i think I’m not gonna fail that test tmr!
OH my gosh thankkkk youuuu too muchhhhh helps me lots.
Thank you so much! I was googling how to divide surds when I glimpsed at the title of this video. I did n't even need to watch the video...(whisper) the title says it all.
do you know why some answers could be simplified to decimals but some can't? Can you explain it to me please that's all I don't know
@@utea5548 This is because some surds are best defined just as they are, in terms of accuracy. As some surds when simplified, gives us recurring decimals, which would be inconvenient and inaccurate to write as decimals, which is why it is better to leave them as surds. Mathematicians are lazy, you know.
@@elishagunasekara4038 tysm u a live saver
@@utea5548 Glad, I could be of assistance.
Due to the epidemic, we sort of learned this on Zoom😂 And now Im gonna have a test on this😭😭😭 = failed the test😜
Can you PLEASE do Dividing Radicals??
Thanks! I forgot during the summer!
Thanks sir this video help me a lot to be honest I am still 7th grade but I like theses kind of problems
this man has taught me more than my teachers legend
I just solved my home work thanks you 😊
I have a question; do you do the same thing if there are two square roots in the equation? For example like:
2
-
√2 + √7
Thank you so much!
Since they are both square roots ( as opposed to one square and one cube) you add them together to get 9 as the radicand.
@@samanthawales5471 i appreciate the help a lot but i graduated high school now
@@sa.rahtonin Lmao and you know that this guy is trolling right?
@@araitol3935 wait really? looks like I still need the help then 💀
@@sa.rahtonin you can't just add the square roots
fakkkk i have test on this next day
sane,
Same
@@piercevictorio534 He's a good man city winger
I have a test today pls help 😟
Did you pass?
Thank you, I got it :)
Rationalize the denominator very clearly Know about thanks for make this video it's a nice video
Thx a lot! This really helped! :D
Ugh... You make it so easy to understand hahaha. Thank you so much
when you reach GOD mode in math
0:33
Thanks for knowledge
DUDE THANKS U SAVED ME UR THE BEST I LUV U
AHAHAHAHAHA
Now that's what I call a Neat trick
Though technically sqrt(5) times 2 would be equal to sqrt(5) times sqrt(4), which would equal sqrt(5 times 4) or sqrt(20), and from there you can rationalize without the conjugate.
Omg thank khannn you make it solo much easier to understand
Thank you khan academy.
shout out MATHSPAPA calculator for showing me this video💖
We know that (a+b)(a-b)=a^2-b^2 but is it same for (a-b)(a+b) I mean is this formula commutative??? Can anyone tell please
Thank you helped a lot
I completely understand this now! Thank you!
HAHAHAHHA
god bless khan academy
8:52 TEN...... TEN......