01 - Simplify Square Roots with Factor Trees in Algebra (Radical Expressions), Part 1
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- เผยแพร่เมื่อ 21 ก.ค. 2024
- View more at www.MathTutorDVD.com.
In this lesson, you will learn what a square root is and why they are important in algebra. We will learn to simplify algebraic expressions that involve square roots by using the concept of a factor tree.
A factor tree is the process of determining all factors or a number or algebraic expressions. Once we write the factor tree, we can find the square root of the expression by looking for pairs of numbers in the "bottom" factors of the tree.
My professor went over this whole video in 5 minutes in class then moved on to more complex curriculum leaving me lost for the next 3 hours. I need the long form explanation like this video because I need the "why you need to do this" not just "how to do this" explanation to learn it. I love this format, thank you
You are very welcome. And yes it’s borderline criminal to go over this material in such a short amount of time. It basically makes makes it impossible to absorb the information.
I can relate to your comment Juan. Only later in my life after doing Maths and computing at uni....and struggling...but then actually working out what worked for ME...do I now love math! Ive now been a math and computing teacher for 20+ years but honestly...whilst I love math, its not always been easy as it is for some people. Thus...I strongly encourage all my pupils to make sure they show HOW their steps to a solution...it really helps them 'get it' then!... btw, my favorite math areas these days are Algebra and Calculas...but I really like Quadratic stuff too!
Thank you. The video has helped me
Excellent explanation executed perfectly. Thank you so much!!❤
It is because they don't even know how their selves. When you go to college and you are smarter then the professor. I took all my college math classes on VHS tape in one semester. How do you know your order of math operation. If you know it as PEMDAS then I have a better way.
Many of us were lost in high school math due to a rapid curriculum. Your method provides depth and understanding by repeating fundamentals. Thank you, sir.
Thank you very much sir ,for good explanation about mathematics,
Hey, man. I really appreciate you putting these videos out there. I’m 31 and I’ve always been discouraged by math until I found videos like this. Your channel with all of these other channels is like a modern day Library of Alexandria. So, thank you for all that you do to educate.
Im 38 and I find this channel absolutely amazing!
I never did very well with math until I started coding web applications quite a while ago.. 15 years ago maybe more (oh man how time flies) anyway Im trying to get into game dev for personal enjoyment and my maths sucks! This channel is a blessing!
@@phutureproof Same here and I'm 52 ! I never went beyond intermediate algebra. I felt intimidated by algrebra, geometry, etc. and so took Business Math and Accounting in H.S. to meet my math requirements. Now that I'm older, I enjoy math more and have more patience to learn it.
I concur my friend. Im 32 and bribed my way to a high school diploma. I learned how to get in trouble in school and that's it. Now I'm back to the drawing board (white board) definitely grateful
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I'm 23 trying to learn math from the ground up. Been using khan academy so far and got stuck on this section and then I found this video. Thank you it helped so much! :)
omg i used khan academy too and came here also getting stuck at this part 😭💀
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Me 3!
this guy is a great teacher . I have learned so much from him in a very short time, an i am 78 yrs old.I will have my grand kids watch and learn from him.
Sir i respect you a lot for making this video. My school and tusion teachers only explained this on the surface and i always wanted to understand what was going on behind the scene. They all explained just the steps, like they were reading from a script but you made sure to explain what your students really needed to know.
I wish you were my math teacher when I was young. You broke it down by detail to detail. Thank you so much.
Having access to a teacher like you you is such a relief. I have to sit through a 4 hour online lecture every week wasting my time with a guy who simply does not know his stuff. Hopefully he will watch your videos :)
These are the absolutely best math videos on YT. Beautifully explained.
Hi
@@michaelaedwards1980 hi
Sorry don't comment
I have just went back to college after many years and I LOVE THIS INSTRUCTOR!!!!
It's absolutely new to me, I wonder in which grade was I suppose to learn this. Got it. 🙏 Mathematics made easy.
You are never too old to re-learn it again, or even come to new insights that actually work, haha...it's all about keeping calculating...
We don't discover, we just document as humankind
i love the fact this dude just roasted the heck out of school textbooks.
Lol
Yo all 63 dislikes must be accidental
@Jayson Bourne More like all of the people that disliked are teachers lol
was
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That's what I can call a real maths teacher. Thank you
This man is a genius! I probably wouldn't be able to explain this to someone who doesn't know it in the same understandable way he did! Bless you! T-T
Thank you. I am 27 y/o studying for gmat and this rings the bell of what i’ve learnt during high school.
A massive heart felt thank you for taking the time to explain this fully and in depth.
This lesson was a "light bulb turning on" moment for me. THANK YOU!
31:40 and 33:25. The square root of 10 squared equals the square root of 10 times the square root of 10, which equals the square root of 10x10, which equals 100. The square root of 100, then, equals 10. That's the algebraic reason why the two operations "totally disappear" and they "undo each other." I think that at the start it is important to write it all out long form so you can see the reason behind things, rather than skip ahead to "this undoes that," and "this cancels that" and so on. Because you can get in trouble quickly when things become more complex if you don't know the fundamental reason so you can recreate it. It's a nice video but a good professor will catch you out if you can't write it all out and know the precise reason (and also name the property which permits it, such as commutative, distributive etc.) rather than saying, "well professor it just..makes it go poof."
Unbelievable... At the end of this Video, All of the equations made sense. Thank you!
You, sir, are an awesome teacher!! Wish I'd had you as a teacher in high school. :)
You're a good professor. You explain it clearly and we understand and could follow them. Thanks and need more Math illustrations like this.
What a difference a good teacher makes!
I really love your teaching. It makes the lesson seem so easy. THANK YOU!
My grand-daughter is getting into this in school. Time to brush up. This is an excellent format to bring it all back. Not only that but I find the course and format very enjoyable. I wish it was so much fun 50 years ago. Thank You for this excellent course.
Hello, thank you for your dedication and love for teaching. Appreciate all your lessons. Ty
You're far better than actual school.
Thank you for sharing your knowledge.
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Hi
i absolutely can't thank you enough for this. I'm in college 10 years later taking college algebra and was lost in the sauce until this video. actually, breaking it down step by step it's clicking in my head. you dropped this king 👑
Finding the square root using prime factors is the best way. it might take longer than other maths 'tricks', but it gives the full picture and it is easy to understand.
Ive been wanting to find a concise and comprehensive ‘lesson’ on finding ‘square roots’, .. this came up. Bang! Does the job! Ty!!
Welcome!
I agree with Juan's comment below. I went through several videos of how to find the square root of a number and yours gave the best example, albeit some areas needed a bit more explanation as to 'why'. Furthermore, I did this to help my granddaughter and to show her how to look up information in TH-cam vids. Thank you very much!
You have made this so much easier for me.....THANK YOU!!!
I needed to brush up on this. Your video was both easy to look at (in terms of visual clutter and organization and lighting) as well as clearly explained. Thank you.
Thank you Tammy!
You are just exceptional and incomparable sir . I esteem your great numerical prowess
I learnt more in this video than 5 of my math teacher classes
IT'S BECAUSE YOU'RE MUCH WISER NOW THAN YOU WERE YOUNGER THEN.
What a great teacher!
It feels like an actual class
True
THANK YOU Professor!! I'm going back for another degree in college; my first degree required Business Math which I passed. This next degree I'm wanting to earn requires Algebra and perhaps Calculus. In high-school I couldn't concentrate in algebra because of having PTSD. I passed with C's but it required summer school every time. I've watched three of your videos and you're a very good teacher. Again, thank you for your time and effort in making these videos. I have more confidence that I will do better in college algebra now that I've found your channel.
I never did get this until now. Thank you.
Thank you sooooo much for making math soooo easy! I had a phobia to numbers until now! 🥰🥰
best math video ever i dont even need a teacher anymore thank u so much
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For sq root -36, why stop factor tree at 6 . -6? You could have pairs of 2 or three. Either 3.2.2.-3 which has a pair of 2s for 2.sq rt -9 or you could have 2.3.3.-2, which has a pair of 3s for 3.sq rt -4. There's still no real answer but it's reduced two ways.
Great for beginners and as a refresher! No extraneous talking....straight to the points! Thank you!
I love the lesson. ..the topic was giving e a headache but after ive watched this I feel its much easier than I could imagine .....5 stars
it's so easy to understand. a very good teacher indeed !
For working factor tree, good practice is to find the largest number, OTHER than one, to start the tree work.
Seriously thank you so much!! My videos for my algebra class did not explain this well and FINALLY found a TH-cam video that helped!! Please keep posting!! Will definitely be back to look for more videos!! :) :)
thank you for teaching and you are a great teacher
I always love math but I have forgotten bec. I don't use it. This is fun just to review math or learn it the first time. Great teacher.
Watching these video's and 'getting it' makes me regretful that I didn't care or apply myself in school. I always just thought I was a lost cause. Having the right mindset is equally as important as having the right teacher.
Sir your technique is brilliant god bless you have a good day I even didn't look it math but after watch yours video I am now capable to solve different equation life changing moment for me Sir thank you very much
Thank you!
omg thank you!! had a light bulb moment! you're brilliant!!
This was an amazingly useful lesson. Sir, you are a lifesaver
But. with no disrespect, intended, did anyone else get Princess Bride vibe when he was doing the bit about the square root of -4?
I half expected the it to go "So Clearly I cannot chose -2! Truly your logic is dizzying. Wait 'til I get started! Where was I? The square root of -4?"
It made me laugh and relieved some of my math anxiety, so thank you again!
Any series for square root like Taylor series
Are Taylor series are tailored for any problems like efficiency power endurance performance with respect to it's size ?
I have always had trouble factoring trees in the past until this guy's presentation. I now factor any number without having to think about it too hard because this dude is a factoring gawd!
Thanks for the tutorial
Sir! you have the great gift of teaching! thanks!
Great teacher. He makes it so simple.
I have also leaned about orphaned number as well. Thank you again :-) m a fan of yours.
Thank you so much. I was having trouble understanding how to find the square root of a big number or an irrational number. This helped me so much💡
thats why all 540,999 are here
Thank you this is what I was looking for. Excellent video lesson.
This teacher is excellent!
I love your videos. I didn’t understood what’s a square root, but after this video I understood what’s it… thank you
Best of the best ‼️Thanks for your amazing videos and amazing teaching ‼️
Thank you!
Very helpful.....great explanation!!!! Thanks
Where can I find part 2 of this algebra (radical expression)? Thanks
thank you, this was helpful as I am homeschool my son, I have a better understanding of radicals and radicands
My second lesson of the day. Very interesting. Thank you.
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Out of all the videos I watched this is the one that helped me.. Thank you so much!😉
thank you for this explanation sooo HELPFUL! :)
Follow me on my channel (Math puzzle &is 1+1=3) a lot more coming ahead
th-cam.com/video/l-voGCM35PM/w-d-xo.html
th-cam.com/video/XjWIzD10Ox4/w-d-xo.html
You are the best teacher i have ever seen
You’re a great teacher!!
I always find it helpful when building factor trees to start with the lowest prime numbers first. I feel that if you start high then miss a factor then you end up with factor trees that look ‘lumpy’ they aren’t wrong but I just find that they don’t look right lol 😆
Thank you very much i can understand now totally worth watching this whole 42 min lesson👍
I just started grade 6 and knew nothing about square roots at all, this guy made this chap look so easy, thankyou so much 💞💞
Wow! I adore your teaching so much
Thank you for breaking it down. I was stuck and now this makes perfect sense.
Just like the other subjects videos, well indepth explanation of why and how, the small details is what makes the difference.
Thank you so much
So very glad to have stumbled on this .
I have been trying to teach my 6yr old .This method is absolutely perfect.Thank you Sir.
Wowww, the thing that I don't understand while on Junior High now make more sense 😂😂😂😂
Love it the light at the end.thank you.
Interestingly, in courses of maths we learn in ex-USSR countries we use the term "arithmetic value" for the principal value of the square root, of course we use principal value as well, but later, mostly in the course of Complex Variable Calculus (Analysis), when complex numbers come to a stage. For both neg. and pos. values we use the term Algebraic value of the square root. I wonder if you use those?
i was thinking with -36, couldnt you simplify to -2 * 18, 2* 9, 3*3. then turn it into (3* √-4)? or even -36 -> -1 * 36, 6 * 6 = (6*√-1)
Dude is the David Malan of Math. World Class education style. thank you.❤
I like your caveats, regarding the existence of imaginary numbers, so that the student maintains an open mind, regarding the limitation to the present work; e.g. the words: imaginary, not real vs. no answer.
Principle Square Root. Thanks for this!
Helpful! How about this hypothetical. Suppose you have 2pairs of twos and 2pairs of threes. Ex. (2.2)(2.2.) , (3.3)( 3.3) what would be the final answer, and how did u derive at such? Just curious to see if my answer is correct. Thx
I cannot thank you more than enough sir
Ever plan to make
Non-euclidean Geometry videos?
If so it would be a far ways down the road. Differential Geometry is very interesting, but very mathematically complex.
Thank you for this video! I really understood what you said
Thank you! Thank you! My 17 year old daughter is studying for her GED, and she doesn't remember how to do this. And I never learned, we didn't have this back in the 90's. (Didn't have to take algebra) (is this algebra? Lol) Anyway, we googled, watched videos, and it wasn't clicking. You made it click. Thank you so much. I can't afford classes at the moment, so u r God sent. 🙏🏼❤️🍷(The wine glass is because I had to drink my Cab, so stressful before, lol) Look at my grammar, u teach English also? 😂 So many GED subjects to learn.
Thank you for such a lovely presentation-I’ve been trying to brush up on square roots and I favour the factor tree for solutions, could you help me to understand though why the Square root of 40 is equal to: (2) square root 2.5. Putting 40 into cal. The answer is 6.324?? what am I missing? Thx for your help-Ken
Clearly understood thank you so much
Great video. Learned more on this video than I ever learned in school.
thanks😍😍
EXCELLENT! TALKING IS GOOD! THANK YOU FOR TAKING YOUR TIME.
At 31:56 , the way how I proved my answer was different. I took the pair of 2s then multiplied them together to = 4 then i did 4*2=8 then finally 8*5= 40, practically saying 2²*2*5 = 40. I also checked my answer for the problems prior to the one you talked about in the timestamp by multiplying the pair of 2s which = 4 then did 4⁴ to equal 256. Then taking the pair of 5s & 3s to get 25*9 = 225. My method seems pretty full-proof to me (im still a student though)
this was just great. thank you.. helped me out a lot
Thank you! This was very helpful and refreshing !
You are an absolutely incredible teacher!
The explanation is precise. Great maths.
Good Day, Sir. A very good lesson. Explained well, Sir. Thanks for your video.