How to Simplify Radicals (NancyPi)

MIT grad shows how to simplify radical expressions, specifically square root expressions, into their simplest form ("Simplified Radical Form" or "SRF Form"). To skip ahead: 1) for a PERFECT SQUARE under the root like sqrt(16) skip to time 1:29. 2) for a SMALL number under the root that is NOT a perfect square like sqrt(32), skip to time 2:45. 3) for a LARGE number under the root, such as sqrt(343), skip to 5:14. 4) for a PRODUCT, meaning a number times a square root like 5*sqrt(54) skip to 7:30. 5) for a QUOTIENT, meaning a number divided by a square root like 4/sqrt(2), and where you have to RATIONALIZE the denominator, skip to 10:10. and 6) for a more complex QUOTIENT example like (4+sqrt(3))/(5-sqrt(3)) where you have to multiply by the CONJUGATE to simplify, skip to 12:36. Nancy formerly of MathBFF explains the steps.
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For all simplifying radical problems:
1) First try to find a perfect square number that divides evenly into the number under the square root. Perfect square numbers include 4, 9, 16, 25, 36, 49, etc. because they are squares of the numbers 2, 3, 4, 5, 6, 7, etc., respectively.
2) Separate the root expression into the two numbers you found as factors, with each number now under its own square root symbol. For example, sqrt(12) = sqrt(4) times sqrt(3).
3) Keep simplifying. The square root of a perfect square becomes just a number, without the radical square root symbol. sqrt(4)*sqrt(3) becomes 2*sqrt(3).
4) Check to see if anymore simplifying can be done, either by combining constants or finding another perfect square number that divides evenly into your factors. If no more simplifying can be done, you have your final "simplified radical form" (SRF) answer, 2*sqrt(3).
If there is a square root anywhere in the DENOMINATOR, you must "rationalize" the denominator, in other words, somehow get rid of the root in the bottom, in order for the expression to be considered simplest. For example, if you have 4/sqrt(2) you must use the trick of simplifying by multiplying the expression by sqrt(2)/sqrt(2). This will clear the square root in the bottom. If you multiply straight across, you would get 4*sqrt(2)/2, which simplifies again to 2*sqrt(2).
If you have a more complicated fraction with a square root in the denominator, like (4+sqrt(3))/(5-sqrt(3)), you will need to use the "conjugate" to simplify. This means multiplying top and bottom by the expression in the denominator, but with the middle sign flipped. Here you would multiply by (5+sqrt(3))/(5+sqrt(3)), multiply straight across on top and bottom using FOIL-ing and distribution. Some terms will cancel in the bottom, leaving you with a simpler denominator that has no square roots.
For more of my math videos, check out: nancypi.com

[@johanliebert5845]

This 17 minute duration video helps me alot than a 1 hour lecture of this lesson

[@bonks886]

Daniel Jon true

[@The_Doctor-xv7kb]

This is ridiculously true😂

[@rimshahaider6903]

I hve been going crazy for day looking for video tht teches me square root but this video cleared my concept, im prepring for tasc test

[@jaynaruecker7142]

Agreed

[@hooralaeenalshamsi500]

X7 Soldier trueee

[@andreboudreaux3419]

having to watch these during corona bc my teacher didn’t put notes 😂

[@havefaithinjesuschristjesu1359]

Andre Boudreaux same

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Andre Boudreaux ikr

[@average_ttv9290]

Same

[@huh481]

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[@Reese9873_]

same omg

[@Autumn-uh9ss]

You explain math in a way that’s calming and straightforward. I’m horrible at math and panic when presented with math problems. I’ve had tutors actually laugh at me for not understanding. I’m cramming for a final and I’m so glad i found your video because I finally understand the content. Thank you so much.

[@yusufkaya1393]

well actualy its a problem she was so calming that i almost fell a sleep

[@judithhill1634]

Nancy you are a natural teacher, you explain every detail.

[@lealoha2168]

before watching this I was just a square.. but now i'm a perfect square

[@vincentlenart1697]

Lmao... that was great!

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That’s beautiful

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What does this mean????

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that was so beautiful

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nice one

[@vincentortega4284]

Thanks, Nancy, you explain math so clearly. God bless you, Nancy.

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Preach

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Hallelujah

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I really love Nancy teaches she has a wonderful calm voice that instantly draws you in to the end. She has a very great vibe that she spreads out. If she had a class i would definitely take her class.

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Simp

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💀 💀

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Ok buddy 😅

[@alycekoran2136]

POV: you're watching this video cause you have a final tomorrow

[@shadeling]

lmao I have a test TODAY

[@der._.krieger]

@@shadeling wtf same

[@der._.krieger]

@@shadeling btw howd yo test go?

[@shadeling]

@@der._.krieger actually pretty good! btw good luck on yours!!!

[@mrpaisanoyt1279]

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[@coltonwilliams1559]

can she write backwards or something??

[@calebcreates8555]

She probably just horizontally flips the recording afterward :D

[@NYsummertimeCHI]

Game Jam! Ah, clever!

[@bmeetze]

Colt_Fourty5 And left-handed.

[@petraarkanian7841]

This what I was thinking... :/

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I just thought she was left handed

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Oh my sweet Jesus.... Why can't all my teachers be like you?

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Van Halen says it best.

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you're old bro.

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She protec She attac She writes bac (wards)

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nice lol

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omg nice lol xD

[@Rayram555]

Nancy is so good at communicating her subject , that I was finally able to see the light . Thank you Nancy!

[@sophia2409]

Ma'am I'm literally grateful to you. This has driven me insane and has caused so many mental breakdowns. Just thank you

[@gregdeane8937]

Excellent explanation. Pleasant to hear your clear articulation. Good teachers are a great blessing.

[@ClaraRodriguez16]

Your voice is si soothing, it helps with the anxiety before tests♥️ thank you

[@camdenelijah]

I swear Mrs.Nancy you just blessed me I almost gave up on math.

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Camden now u gave up, no?

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If I had this math teacher I'd pay attention every day in class. Not just because she's beautiful, but because she's so good at explaining that she deserves my respect. Thanks so much for the vid!

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Down Horrenusly

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Down judgementally

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Down respectfully

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@@annabruce5194 Are you as pretty as Ms Nancy pi?

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ur comment made sense till beautiful. kidding

[@rowantree101]

I am using parts of this video in my Algebra One course Nancy, your even and deliberate pace is perfect for a classroom activator! Thanks!!!

[@gameclips-thelegend4109]

Chris West how to not do your job lol

[@roroo]

@@gameclips-thelegend4109 teachers show videos all the time to show students and also learn off of to be able to reiterate the idea 🤷

[@debraarizona4809]

Nancy, your video was very helpful. I never understood how to simplify radicals. Watching your video has given me a better understanding. Thank you for sharing.

[@jayyyzeee6409]

@NancyPi, I'm impressed by how much info you include in the notes. Great job! I used to tutor math students, and saw so many people failing with the algebra. It's nice to see you emphasizing those things. I always emphasized liberal use of parentheses to help students with sloppy habits.

[@kristinaschaller1242]

saved me as a new "homeschool teacher" for an 8th grader.....way too many years since my algebra days!

[@hanaoh2936]

why did this help me more to understand than my teacher?? 😂

[@aznmayo]

cuz she cute lmao

[@clorox3595]

She hot asf lmao

[@vaderonzerodegreezz4206]

She explains it better

[@anastasiaboofenheiser8125]

Thank you so much!!!! I watched 2 videos b4 yours and was still lost. You explained it wonderfully and now I finally get it!

[@Dragerguy]

Watching her explain math is one of the most satisfying things ever especially since she’s really pretty

[@Drforeverok]

😂 i was looking for this comment

[@MuhammadYusuf-eq8xi]

@@Drforeverok same

[@joejaffe4604]

Excellent video helped me brush up on math I haven't used in a long time...thanks, and keep up the great work Nancy.

[@rodrigoibarra613]

You are the perfect combination of beauty and brains. You just won another subscriber. BIG THANK YOU!!!!!!

[@mccarthyroderick]

Damn, why can't all math teacher be this good!! Amazing Nancy!!

[@thelifeofme5221]

Thank you so much. I am online, and this was one of the hardest lessons. I googled for help, and I came to this video. Understood it in a few minutes, rather than hours. You are a life saver.

[@cheshire__kat]

Thank you so much! I honestly completely forgot about it and I didn't know that I'd be needing it again very soon. You're great at explaining~

[@RoshanLamichhane]

Nancy can you make videos that can help people taking the SAT or the ACT

[@camilasummers]

Thats me .... Taking it tomorrow

[@charliekowtarapu3803]

Same

[@capie44]

You are asking ALOT! I am helping -- er, struggling with 40 year-old education...to help my 13 year-old to prepare for the SAT. But I am in there with you! HELP!!!

[@maddiepaddy2608]

@@charliekowtarapu3803 this was a year ago- did u do it??

[@maddiepaddy2608]

@@camilasummers this was a year ago..did u do it?

[@that1queeralien]

this video is by far the best math video i've ever watched. videos usually never help me, as i can't keep focus, and whenever i don't understand something the way teachers explain it. my class learned this while i was away (due to hospitilizition) and i never learned how to simplify radicals until now. thanks so much

[@Givenhanchabalika]

I like the way she does it calmly

[@paul-thestupid1761]

Thank you, Nancy, Your delivery is awesome.

[@rezascorner2091]

Oh my god. Thank you so much. This was so clear and taught ne so well. I needed this information for an Algebra 1 test tommorow. I never even slightly understood what the teacher meant. This helped so much. Thank you so much.

[@bekah760]

I am honestly so grateful!!!! I almost cried thinking I was never going to understand. You rock! I appreciate the time you put into this. I am definitely a follower now ❤️

[@thesweetestjp]

My teacher taking an hour and this woman explaining more in depth than my teacher in just 17 minutes

[@ken3564]

omg thank u so much i have watched so many videos and was still confused until i came across ur video. i finally understand it, honors geometry is a pain. thank u so much nancy

[@pro-films9920]

17 min video which is surely better than a 2hour lecture. Appreciated :))

[@RinoKiiu]

I have a teacher that couldn't teach for their life. You just helped me out because I was almost on the verge of crying my eyes out. Thank you so much!!

[@jiaichigo5863]

This is where I always go every time our math ends cause honestly, she's gradually teaching us the steps and that's what I like about her.

[@spergplayzxx]

I was having trouble understanding how to simply radicals in geometry and this video was very helpful.

[@susanchen5220]

thank you. i understand so much more now

[@angkorwat6480]

I dont understand

[@PedroFlores-id5pm]

Thank you so much! I really understand and love your voice. Very clear and doesn't feel rushed.

[@sagesonarry6521]

Well aren't you just a savior. I've understood this in just a few minutes. You'd make an amazing lecturer, I think everyone agrees.

[@mehriabaza795]

Thank you so much for your video. Finally I’m starting to understand the concept. Thank you for breaking it down and taking the tome to explain each step slowly and clearly.

[@marysianaisaya7098]

Yeeeeeeees its good

[@jackjackc5011]

how come my teacher will sit down and fail to teach me for 2 hours but I can fully understand this entire lesson in 15 here? Your awesome

[@RedRedMCmusic]

studying for the asvab over here and im happy i found this beautiful math teacher. had me refresh my math easier than i remembered in high school

[@dylanm3181]

couldn't wrap my head around knewton's explanations. Was about to lose my mind. Your calm and steady voice did the trick. Hopefully i'll be able to complete my assignments thanks to you

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nancy for president

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Better than what we have now

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Eriq Brown hell yeah!

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D3lete more like Obama for President again

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Orange man bad!

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I lve u

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This is legit the most helpful vid on the internet

[@kylieloomis7761]

Thank you for making it so much easier to understand, I was so lost, this helped so much!

[@MegaMeanDean]

For some reason, I was struggling with this. Thank you NancyPi for explaining it in a way where I do get it now.

[@samizin911]

I don't know why but as a portuguese speaker (I live in Brazil) it's easier for me to watch an english lesson rather then a portuguese lesson. Is this strange?

[@marcelocalenga5573]

@@leonardozika2648 oquê? Kkkk

[@ArcherAC3]

Totally not, same thing with me (also Brazilian). Perhaps it's because, as english is not our first language, we just happen to pay a little bit more attention to the words and this results in a more focused learning?

[@ArcherAC3]

@leonardo zika Mds, BR tá em todo lugar kkkkkkkk

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@@ArcherAC3 eu sou Angolano🇦🇴 kkkk

[@fuinhaamiguinha8932]

@@marcelocalenga5573 Oloko

[@bobcrachead3402]

I love the fact she’s talking slowly so we can understand her better,must be painful.

[@kaduflutist]

Thanks, Nancy! I love your teaching 'cause you look for simple ways to make it understood.

[@keithmansfield1844]

Thanks for your videos!!!!! I have been sharing them with my Algebra class for remote learning in NYC. Keep it up!!!

[@jaketruell3584]

*does default dance*

[@sami8411]

Jake Truell pew new new new new *claps*

[@pumpkinspice2116]

Thank for explaining it easier

[@padnofred4755]

This is like the best maths lesson I've had since my year 1 in college thank you God bless and motivate you to keep helping us in mathematical nightmares

[@kevin21046]

5 years and still helps me out. Thank you everybody for not changing math

[@anactualbird6801]

Thanks so much for this I missed the day my teacher taught this lesson

[@akshitsaxena6220]

You're the best! 😊

[@jackieb5031]

so patient and takes the time explain operations so they make sense. thank you so much

[@emileeladra9568]

I learned this a while back and forgot the process, but you easily jogged my memory! Thank you!

[@DavidPerez-tj5jw]

She's an angel

[@danielmillan6144]

Thanks

[@lloydkline6946]

My favorite algerba teacher, and the prettiest professor

[@nilesgray2319]

I have used this video to teach this for years! Thank you so much!

[@ashmitagurung7208]

the fact that i can actually understand this is crazy

[@Gjaurequi]

Thank you Nancy! You have refreshed my math memory on the conjugates. Also, wow... Try quenching your thirst by drinking some H2O boys !!!

[@RichardLifts]

love how this taught me more than my math teacher has done in the past year and a half

[@sugarrushjoe3621]

Mad respect to you being able to write backwards in every video

[@operatorbutt4265]

I watch this purely for asmr

[@jaynaruecker7142]

Lol same

[@deeceestudios5875]

literally nobody asked 😂

[@ascendeddoge6080]

Mood

[@onetwo234]

@ZI TING ZHENG It's not called cringe section for a reason

[@themostviralofalltime]

learning asmr

[@SuperNazaar]

better than my professor, i feel you are injecting math in my mind.

[@aidanschnittker2455]

Thank you SM Nancy, You just taught me more about radical expressions then my teacher did all year

[@beckywaytoomuch]

Literally the best explanation I've found on the interwebs thank you

[@brrrr6599]

A beauty gifted with knowledge

[@Gjaurequi]

Gifted? Lol She practiced. A lot.

[@smellytaint]

15:10 it's faster to just use (a-b)(a+b) = (a²-b²)

[@John-lh7st]

bro idk why her voice is so smoothing and relaxing im boutta fall asleep while learning this lmao

[@melissacheckland8243]

Your videos help me so much! Thank you! Keep 'em comin!

[@squidwardtortalini160]

Anyone else realized that she had to write all this stuff backwards, in order for us to see it normally? I find that impressive.

[@maizahkhan9244]

No they edit it 🤦‍♀️

[@shiwastaken0]

Yeahh pretty sick

[@MrStatguy76]

The square root of 16 is plus or minus 4 not just positive 4. -4*-4 is also 16.

[@VikasGupta-ql6qq]

Noob its not +-4 its +4 only😂

[@austinmyhre4513]

It’s implied to be the principal square root.

[@taytay1550]

This was so much more helpful than my teacher!! Thanks

[@sirinecherkaoui8265]

Thank you so much Nancy! Your videos are so helpful.

[@PIXELGamerzXvlogs]

why do i feel like whenever she takes a pause she's going to say 'but'.

[@bananapopproductions1292]

How does she right backwards so well TwT

[@mairkcify]

Hint: She's not left handed

[@bananapopproductions1292]

​@@mairkcify still confused

[@bananapopproductions1292]

@@mairkcify I'm guessing she flipped it? lmao

[@pasiaomega3868]

OMG thank you for saving me from a night of weeping over my trig homework, because it's been a hot minute since I worked with radicals.

[@SpeedySebas]

Same this isn't even my first time learning this I'm also doing trig but I forgot how to simplify radicals

[@pingmendoza719]

Much better than a week of lecture on radicals in school!

[@hawkeyeaerialphotography6652]

How does she write backwards

[@buggy997]

OMG IS SHE WRITING BACKWARDS😄

[@cheesecake9178]

Buggy 99 maybe but I feel like she just horizontally flips the recording after she’s finished as others have said.

[@Gone4Everx]

@@cheesecake9178 it would flip her hand too no?

[@yuhyuh5674]

@@Gone4Everx that's the point, she's writing with her right hand, so when it is flipped it seems as though she is writing with her left hand

[@shiwastaken0]

OMG you are a goddess I have a Radicals test tomorrow and this helped soo much, thank you!

[@autoelite8482]

Well, this is the first time I’ve subscribed to a math channel.

[@sofia9127]

please do videos on iequalities!!!

[@industrialsystemsptclass2212]

Great job

[@nadeemurrahman5688]

I really appreciate your method of teaching math. Please, keep it up.

[@cordelw7600]

Thank you, your videos make a huge impact

[@HeSo_71]

ok do you really write mirrored so we can see the numbers in their actual form? holy

[@Jurkblot]

dude all they have to do is just mirror the final the video

[@Albertobelmonte9]

Yay

[@michellecarlon5480]

Very helpful video! She explains each step very clearly...thank you!

[@PatriciaRiveraLaBlogger]

Such clarity! Thank you.