Simplify a radical expression with variables

👉 Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that are the same. The term of the product is the required square root.
When the radical cannot be conveniently decomposed/factored into two same terms, we factor the radical into a product of a perfect square and a non-perfect square. Using the product/quotient rule of radicals the perfect square is evaluated and the non-perfect square is left as a radical.
👏SUBSCRIBE to my channel here: www.youtube.co...
❤️Support my channel by becoming a member: / @brianmclogan
🙋‍♂️Have questions? Ask here: forms.gle/dfR9...
🎉Follow the Community: / mrbrianmclogan
Organized Videos:
✅How To Simplify a Radical Expression
• How To Simplify a Radi...
✅How To Simplify The Cube Root of a Number
• How To Simplify The Cu...
✅How to Simplify The 4th Root of a Number
• How to Simplify The 4t...
✅How to Simplify the Square Root of a Number
• How to Simplify the Sq...
✅How to Simplify The Square Root of a Number with Coefficient
• How to Simplify The Sq...
✅How to Simplify Expressions | 4th Root
• How to Simplify Expres...
✅How to Simplify Radical Expressions | 5th Root
• How to Simplify Radica...
✅How to Simplify Radical Expressions | Cube Root
• How to Simplify Radica...
✅How to Simplify Radical Expressions | Learn About
• How to Simplify Radica...
✅How to Simplify Radical Expressions | Easy
• How to Simplify Radica...
✅How to Simplify Radical Expressions | Hard
• How to Simplify Radica...
🗂️ Organized playlists by classes here: / mrbrianmclogan
🌐 My Website - www.freemathvid...
🎯Survive Math Class Checklist: Ten Steps to a Better Year: www.brianmclog...
Connect with me:
⚡️Facebook - / freemathvideos
⚡️Instagram - / brianmclogan
⚡️Twitter - / mrbrianmclogan
⚡️Linkedin - / brian-mclogan-16b43623
👨‍🏫 Current Courses on Udemy: www.udemy.com/...
👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvi...
#Simplifyradicals #radicals #brianmclogan

[@brianmclogan]

More Examples Simplifying Radicals - czcams.com/play/PL0G-Nd0V5ZMp53jELWvQp4KFgD-pLmQ0Q.html

[@allahiseternal8422]

I give a big fuckin like to this video

[@LittleRapGuy]

good video

[@californiadreamin8423]

Hello Brian, from across the pond. Excellent video. I’m beginning to realise that manipulation of these square root problems, was a major gap in my knowledge 55 years ago !! when I did my O and A levels and onto Engineering at Uni…..or perhaps it’s my memory 🙀
I find it very straightforward and yet…..

[@abhinavbaral204]

I do better watching 2 min of this than learning for 45 min in my class. Thank you

[@acceptablexy4805]

well i guess you didn't find the video helpful cause it was 5 minutes

[@jasiribandele5601]

Tom Hopkins idm he was joking😭

[@mycavidal7165]

lmaooo same bruh😂

[@vv1034]

Hahahaha same

[@nigelbaraquia3404]

Lol....same

[@definitelynotwalter]

9 years later and still a saviour.

[@preppymaemid4126]

10 years later still goin hard

[@delapenajudieljess1230]

nice pfp

[@Madggs]

10 years now

[@s_squid_s]

12 years later and still popping off

[@zosiaa_officiall]

12 years later still slaying

[@kryo5579]

I'm watching this right before my test wish me luck lol

[@drewelliott3132]

Kryo literally same lmao pre calc

[@kryo5579]

@@drewelliott3132 Ace it man

[@snowangel2209]

Same

[@LastGREATEST0]

Same

[@Jakethegreat182.]

Good luck to everyone here

[@chloe._.ey21]

i srsly was born to not understand math :(

[@elroe327]

Same

[@cerareid240]

CHOGIWAADANABEONENEUKKYEO same

[@gracietara8723]

CHOGIWAADANABEONENEUKKYEO sammmeeee like bruhhh

[@Godakuri]

What's so hard to understand. Explain and I'll explain it to you

[@Godakuri]

This video was a bit more confusing than the others. But you basically want to find two numbers that go into 48. That would be 16 and 3
Square root of 16 is 4, and square root of 3 cannot be simplified. So, 4 would go on the outside of the square root, while 3 stays inside
4 × sqrt 3

[@lucablue8126]

Do you film your lessons as a teacher then post them here? Because that’s brilliant.. never worry about a sick day again.

[@brianmclogan]

yes I do Luca!

[@cydra-evolution5623]

@@brianmclogan bro just cut out parts of the video after you record so students arent afraid of asking questions

[@ZikzakHD]

@@brianmclogan Hey. I'd like to study in your high school is that possible ?

[@rogerbenson9544]

This aged well haha. This is how everything was done for the school shutdowns

[@kokokoko3936]

Our teacher literally makes us figure everything by ourselves as if we know wtf to do

[@kokokoko3936]

this user can't be reached Okay...but this is different. He gives us something we don’t know how to do and makes us do it. If we say we don’t know what to do he tells us to look it up.

[@Alex-rx2cm]

I totally understand what ur talking about. Some teachers just aren't meant to be teachers. Some should have retired already because they left their patience in 1765

[@alexshuparskyy6052]

Just got into 8th grade and i can't understand crap its just so hard for me

[@brianmclogan]

take a breath and slow done, this is not a race, you can understand this stuff, practice and give yourself time

[@BigAirr.]

Feel you

[@aedanmayschak5827]

Same with me but I'm a sevie in accelerated

[@blkout6202]

Im in honors math in 7th grade. So I'm learning this stuff

[@Ry_TSG]

legit ness same. I took algebra when I was in seventh grade as well.

[@sinkidonk8259]

I think this had been the best video I found yet on simplifying square roots with variables, thank you I am trying to study up for a math placement test for college

[@StudyBlanca]

wow, this is me right now

[@eebijeebi6885]

@@StudyBlanca Good luck!

[@jacobhailemariam5068]

nah watch the organic math guy or whatever he has a method which is like 2 steps

[@23vbg]

I do so much better in class because of your 5 minutes videos than sitting for 1 hr in class. Thank you

[@BigAirr.]

My man you have saved me again

[@vishnukikkeri9187]

I need you as my math teacher

[@providence3977]

Say no more - Your pfp says it all :P

[@atavierreed2267]

ikr lol

[@wicked_mia]

When you’re watching this 5 minutes before a quiz 😎 summer school gang😌✌🏼
Edit: I got an A on the quiz!!!😁😁

[@adnankashalo1409]

congrats! 2 months late but still

[@amarehinton5015]

I’m in summer school too

[@Insaneflightreacts]

11 years later and this dude is saving me the night before finals

[@eunosmedia90]

This dude explains it better than alot of teachers ive had thank you

[@tylerm3m3]

you are a saint. bless your soul. learned more watching this than in class.

[@poochi7587]

Still didn't get it

[@marrinarice8658]

math has ALWAYS been one of my easiest/favorite courses, but i have a horrible precalc. teacher this year. he rushes through the steps and he never likes to help with the questions we have. he’ll just say “go watch the video on schoology, but it’s just a video of the notes we did and the explanations on how to do the problems are still weak. then on the homework we’ll have problems with more steps and nothing in the notes helps me. I’ve never had a B- in math until this year and it’s crazy to know that everything matters on how your teacher presents the material to the class.

[@ImLOL006]

Thanks a lot! You are out here SAVING LIVES istg!

[@nikolaskatanjian4226]

Thanks to your videos I got a B on my final👍🏼🤩

[@brianmclogan]

awesome! Congrats to you Nikolas. Happy to be there for you

[@official_lissana2358]

Don’t call this person stupid he tried very hard and a B is not bad that’s actually an 80 الرداعي قهرهم

[@heshamhesh2516]

Official_ Lissana k buddy

[@kchen4896]

Lol الرداعي قهرهم

[@sharmilaallam3455]

@@official_lissana2358 ssssss right

[@tankuser4276]

I dunno why but I smile and sometimes laugh when I see math teachers taking their time thinking. I could visualize their brain sweating from thinking too hard lol

[@manuelmojica8009]

You are a lifesaver. We're taking a quiz on this on Monday, and this video prepared me a lot.

[@user-bl6ux4jt6m]

my final is in 3 hours and you're a quick life saver for all the concepts im still confused on thank you!!!!

[@brianmclogan]

If you sign in to receive my newsletter, You will receive an email from me with my ebook. You can simply respond to that email. I do not want to post the address on CZcams for sake of spam

[@Sultan_A]

🌟🌠 Very Good, Brian McLogan, Keep It Up 🌠🌟

[@jacobdoolittle2044]

Currently Active duty taking online college, pre-calculus was killing me until I came across your videos! THANK YOU!

[@williamestes4169]

You must be praised. I have been looking for a good explanation for hours!!!!! That was what I was looking for thanks. Subbed!

[@1Giorno_1cup]

Bruh wish I had you as my video teacher, my video teacher is just like *writes down and goes over one problem and expects you to know it*

[@laura-yh6fv]

THANK you omg I can’t do math for shit and I’m in 11th grade....going into consumer math

[@RiseAndRenewtoday]

11 years later its even better

[@Azooz70000]

We learn from you from Saudi Arabia teacher. Thank you❤️

[@itslululemons6949]

Watching this right before my test :/! Thanks for the help :)

[@izzyyy9471]

Did you do good?

[@itslululemons6949]

@@izzyyy9471 i got an 100 :)

[@izzyyy9471]

@@itslululemons6949 Yayyy! :D

[@Dr_N0]

@@itslululemons6949 i hope u fail all your classes from now on

[@bzgamer41]

I have a test on radicals and inverses tomorrow. this helped!!!

[@thebestking4615]

This guy is a legend! Thanks so much!

[@skyzlar]

Your videos have saved me- I have a 90 minute algebra class and I’ve learned nothing this year so I have to go home and look stuff up on CZcams.

[@asiaf4914]

THANK YOU. idk why i cant understand what my professor is saying, I just couldn't get it but this really helped a lot. THANK YOU!

[@WeHateAjay]

Ok I’m in 9th grade and I don’t understand how to do -21 radical 27x to the 9th power

[@shaunyjimenez9637]

Same 😔

[@Rasqberries]

11 years later and he’s still a legend

[@KieraClements]

12 years later and still a god send

[@j.h170]

I could go back and rewatch my school's original lesson recording, but it's 40 minutes long and I can't be bothered. This is easier and faster, thank you.

[@brianmclogan]

yes.

[@gabynevarez]

At 5:04 why is there 2 y's in the index and then when you rewrite it theres only one y on the outside im confused

[@victoria-cm6xm]

Gabriela Nevarez BC in algebra, yy would be considered as y^2. Which is y to the 2nd power. So he rewrote the problem so that the y is doubled up? Idrk how to explain it

[@AbeWinkin]

This video has just helped me so much. It answered so many questions. Thanks, Brian.🙂 Now I will like and subscribe.

[@llongdong]

Outstanding!! You should be King of the World.

[@loganayesh5472]

It all makes sense now you’re a genius

[@benbonczek]

Thank you so much!!

[@BRYCEC00K]

Thank you this video was helpful I was absent and this is what we we’re learning

[@bootertrooper3596]

Mr clean comes in clutch every single time

[@saka1029]

√(48x²y⁵) = 4 |x| y²√(3y) You should consider the case of x

[@shen144]

I'm not sure if they have considered domains yet

[@kodyhoriuchi172]

This would normally be a superfluous step because x is an unknown value. Unless it is equal to something, the unknown value x can remain unknown meaning it can be positive or negative when solving. For argument sake, we'll say that it is positive so it's less for us to do

[@mohamedhelal8932]

Right u r

[@omaralhajji540]

Bro ur such a life saver this one example helped more then a whole tutour

[@kzcreationzmore]

This guy explains in under 6 minutes what my math teacher hasnt been able to make me understand in 3 weeks

[@luckymahir5615]

the dude at the end "why didin't you do 4 * 12"😂

[@merkow6711]

This dude teaches better than my Math Teacher

[@mars-nr8sx]

i hate to say this bc my algebra 2 teacher is amazing, but this 2 minute clip taught me more than the hr and 15min lecture did😅

[@alliegrace9948]

this guy a life saver fr

[@Goalafied]

I got a final tmw this is the only thing I don’t understand you just saved me 🎉🎉🎉

[@arkan7rb]

thank u sir
greetings from Yemen

[@InsighterofTech]

Thanks a lot man, really appreciate this video. I didn't understand what my algebra teacher was saying, or teaching at all. I finally understand now, so thank you again man.

[@brianmclogan]

You are very welcome?!

[@abbeyharris7967]

my final for math is tomorrow i don’t get any of the math so i keep looking it up on here and this guy keeps popping up. I get it my teacher doesn’t teach so thank you, be my teacher

[@daynepiscione7748]

ive got a math test on radicals tmr... ill update this when i get the grade back :))

[@ihearthazza4885]

dude this guy has helped me so much

[@evanweglarz9778]

I don’t even try to pay attention in class anymore because it’s much easier just to watch these kind of vids

[@asmodeuszdewa7194]

But this video is wrong

[@Ramesh-ny2ik]

I want to have you as my teacher because my teacher never explains me the way you do like easy and faster way to learn

[@lavaniadelrey2807]

You are a genius

[@chinmayeekatti9781]

I’m watching this in the middle of my test please help me

[@providence3977]

That’s cheating >:(

[@abenezerwondewosen]

wow teacher it was clear for me.

[@emero3665]

At 4:44 how do you determine what variables go outside and what variables go in the inside?

[@scaythe8858]

U must find the square root of each if it has square root then put the square root of it outside

[@evanrichter8141]

yex

[@Moll662]

got my sat next month!

[@mekhaterrence6246]

Thanks brian mc logan

[@troyacker5305]

I wish you were my teacher

[@Siete77739]

I forgot this was a video and I was about to ask a question

[@elaine-mw7li]

a life saver

[@Taught_by_Tebza]

You should indicate the element of principal root by putting x inside the absolute value symbol.

[@thiagoamodio75]

helped a lot thanks

[@brianmclogan]

Glad it helped

[@user-ky5dy5hl4d]

Yes, you can simplify the square root of 6 x 8 further; that is square root of 6 x 4 x 2. But if you want to use it is another thing.

[@Alleksxx]

You can also simplify the square root of 24 × 2 since 4 is multiply of 12 its also a multiply of 24 cause 12 is just half of 24. Also you would get the same numbers (6, 4 and 2)

[@trustnallah8184]

Please note that the square root of X squared = absolute value of X not just X. This is what many people don’t realize.

[@Mariela0183aa]

Can u be my teacher you explain so well 👏😭🙏

[@crissunknown8920]

Army 💙💙

[@kime394]

what do you do if the number under the radical is a perfect square

[@ItzDuhLag]

Kimberly Emile no number will end up on the inside but it’s possible a variable will.

[@vivienreysoriano1256]

Thank you so much!

[@moelester5509]

You are a great person

[@tonyhaddad1394]

Mann you have complicated the problem (its quite easy )

[@serarose6876]

Lmao I know that it’s taken from his last name but can we just talk about how his merch says Logang??? I can only think of Logan Paul

[@marques5635]

Lol

[@laxzazazaza8278]

These vids are god sends,after the online school year,i had no knowledge in my math class due to a mix of it being online,not being able to focus,and being a slacking son of a bitch,only passing thanks to random calculators online,as of current its nipping me in the ass,and yet,these videos are making it possible to survive in my class,and pass no less,despite basically missing a year of math,without these i woulda already been dead in the water man.

[@longbluesquid]

more on fraction form. like i know your denomanator cant be in radical is this correct?

[@glowkami]

why does every other video make us do like 500 other steps when we could literally do this LOL

[@brianmclogan]

No idea

[@Zero-pz4ku]

why no absolute values around y?

[@kimayliahenriques]

thanks

[@Rycethegoat]

You need to include the abs value bars in the case that x is a negative number

[@sahir4341]

THANK YOU SO MUCH

[@richardslater677]

To be honest, I think there is a debate to be had as to whether the result is simplified or more complicated!

[@user-po3jb3gp4p]

deff more complicated

[@micsxii9150]

Thank you sir,im always watching ur videos😁

[@karenina.l]

Shouldn't there be an absolute value sign around x when it comes out of the radical? Even index, even power inside, odd power outside.

[@mdavis3262]

You sr are the GOAT

[@anthonysafo473]

Thank god for you

[@marioivezaj154]

boutta buy all ur merch

[@justabunga1]

What about the use of absolute values? Shouldn’t the answer be 4abs(xy^4)sqrt(3y)? abs stands for absolute value and start stands for square root. If you try to plug in negative numbers and write without absolute values, it would be undefined under the square root symbol. The absolute values can be negative, which would a positive number.

[@asmodeuszdewa7194]

You got it almost right.
The answer should be:
4abs(xy^2)sqrt(3y) which is equivalent to 4|x|y^2sqrt(3y)

[@kaiaeuao]

THANK YOU OMG

[@AdityaMishra-pm3xw]

Isn't the x supposed to be in absolute value notation?

[@user-qr8co6hp4r]

I’m crying, why is math so hard

[@brianmclogan]

Take it step by step

[@sarahdeay7341]

What would I do with a problem like 'simplify the square root of 50xy^2'

[@simone2603]

You do √50x^2y^2. First you find the square root of 50, which is 5 √2 . 5 √2 times x^2 times y^2 which is 5xy^2 √2

[@05w47d]

Yes I have many questions