01 - Simplify Square Roots with Factor Trees in Algebra (Radical Expressions), Part 1

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.

[@JCHP81]

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

[@MathAndScience]

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.

[@B_Evo]

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!

[@felistusphiri-dd8rv]

Thank you. The video has helped me

[@yoliirizarry5643]

Excellent explanation executed perfectly. Thank you so much!!❤

[@glenwardgross366]

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.

[@claireF-14D]

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.

[@adelawilliam1094]

Thank you very much sir ,for good explanation about mathematics,

[@j_jones_]

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.

[@phutureproof]

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!

[@konglives4453]

@@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.

[@hartsgrace1205]

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

[@johnfreewalt8425]

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[@chidiasuke3386]

Wow great job 👏👍👏👍👏

[@lilboiUK]

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! :)

[@moonwon2892]

omg i used khan academy too and came here also getting stuck at this part 😭💀

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[@lindseyrickards7256]

Me 3!

[@georgeholzman6967]

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.

[@jamesb5799]

I have just went back to college after many years and I LOVE THIS INSTRUCTOR!!!!

[@RR-jx4fs]

I wish you were my math teacher when I was young. You broke it down by detail to detail. Thank you so much.

[@Jobanuwu]

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.

[@justinpullen1472]

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 :)

[@abdesay3772]

That's what I can call a real maths teacher. Thank you

[@borowczyk76]

These are the absolutely best math videos on YT. Beautifully explained.

[@michaelaedwards1980]

Hi

[@williamkazungu1411]

​@@michaelaedwards1980 hi

[@williamkazungu1411]

Sorry don't comment

[@weeredvixen8033]

A massive heart felt thank you for taking the time to explain this fully and in depth.

[@lyasweetheart]

i love the fact this dude just roasted the heck out of school textbooks.

[@cvijayshree]

Lol

[@jaysonbourne8841]

Yo all 63 dislikes must be accidental

[@iyaz_]

@Jayson Bourne More like all of the people that disliked are teachers lol

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was

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[@daeshandarosa6297]

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

[@okbutwhy2506]

I really love your teaching. It makes the lesson seem so easy. THANK YOU!

[@Ruvana]

Hello, thank you for your dedication and love for teaching. Appreciate all your lessons. Ty

[@collinmoropa7938]

It's absolutely new to me, I wonder in which grade was I suppose to learn this. Got it. 🙏 Mathematics made easy.

[@TITOFROG1]

You're a good professor. You explain it clearly and we understand and could follow them. Thanks and need more Math illustrations like this.

[@drayhogg53]

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.

[@rauldempaire5330]

What a difference a good teacher makes!

[@TheCarabailey]

Unbelievable... At the end of this Video, All of the equations made sense. Thank you!

[@queenroyalty3907]

You have made this so much easier for me.....THANK YOU!!!

[@ikamaulizan3894]

Thank you. I am 27 y/o studying for gmat and this rings the bell of what i’ve learnt during high school.

[@kirkdsnyder3844]

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 KZbin vids. Thank you very much!

[@jonathanmachado4790]

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 👑

[@seahorse5689]

You, sir, are an awesome teacher!! Wish I'd had you as a teacher in high school. :)

[@alyssaandrews1752]

Absolutely brilliant! You helped me so much compared to the other 15 videos I watched before this! Thank you keep it up!

[@grannysword]

..........***Greetings, Beloved of God. This message is lengthy but, it is very important. The ancient Israelites was tested by the Sabbath commandment to see if they would keep God’s law or no in Exodus 16:4- Do not be surprised if God allow man to do a similar test, enforce some type of Sabbath law to see if we will keep His law or no. ************************************************ Right now, we all do not see eye to eye, but, please hear me out.............. There is no way anyone can prove from the KJV Bible that Saturday, Sunday, etc. is the biblical seventh day Sabbaths. For, the words Saturday, Sunday, etc. do not appear in the Bible. A continuous Saturday, Sunday, etc., “man made Sabbaths” ARE NOT the true Bible Sabbaths because they are not calculated by true time. God’s true time is written in Genesis 1:14. When God commanded us to keep a seventh day Sabbath, kill the Passover on the 14th day of the first month, keep the day of atonement on the 10th day of the seventh month, etc......would He not have given us a calendar/Time to find these dates? Yes, He would have and He did, in Genesis 1:14. We are commanded to keep the days, years, etc. by the lights in heaven (the sun, moon and stars.) God did not specify which days, so, we must conclude that He meant for all of His 3 category of days to be kept by the lights in heaven. *********** The Sabbath command is one of the Ten Commandments listed in Exodus 20. It is just as important as the other nine and God commands us to keep it. Multitudes of people think and teach that we are only required to keep 9 of God’s Ten Commandments. My Friend, if we think this way, we are already deceived. ***The Sabbath is a feast. Leviticus 23:1-3 ***The moon is for seasons. Psalms 104:19 ***The lights in heaven are for seasons, etc. Genesis 1:14 ***The words “feast” and “season” comes from the same Hebrew word, MOED. ***MOED is, appointed times, appointments, feast, season, etc. The Sabbath is a MOED, an appointed time , a feast, a season, etc. Therefore, the moon, along with the other lights in heaven, are for Sabbaths. THE SABBATH IS TO BE CALCULATED BY THE TIME GOD ORDAINED IN THE BEGINNING OF CREATION NOT BY MAN’S TIME/CALENDARS. Who can prove from Genesis 1:14 that the Sabbath day is not calculated by the lights in heaven? Although many have tried, it cannot be refuted!! Take a glimpse at the dates in Genesis 7:11 and Genesis 8:4,13,14. Are these dates calculated by the Time God commanded in Genesis 1:14 or by the Gregorian time or some other man made time? ********** There are about 167 countries that keep Sunday as the seventh day and the remaining, approximately, 64 countries keep Saturday as the seventh day. If there is a “seventh day Sunday law” enforced and the remaining 64 countries change their calendars to read Sunday as the seventh day, then, the world will be keeping Sunday the seventh day as the Sabbath. Mon. Tue. Wed. Thur. Fri. Sat. Sunday Law 1. 2. 3. 4. 5. 6. 7 What day will you and I then keep as the Sabbath? Already today, there are “Sunday Blue Laws” on government books. Man can change “their” time anytime and deceive the world under the leadership of Satan. We must calculate God’s Sabbath by God’s Time so The Great Deceiver can not trick us about the true Sabbath and “cause” us to worship him. “ He will think to change time and laws.” says Daniel 7:25 He only “THOUGHT” to change time when He “supposedly” had replaced God’s calendar with his calendar on earth. For he could not and has not truly change time because God’s Time sits in the heavens where no man can tamper with it! The sun, moon and stars, the lights in heaven, are God’s Time/Calendar. *********** God’s Calendar has three category of days, the new moon day, the six work days and the Sabbath day. 2 Kings 4:18-23 & Ezekiel 46:1-3. The new moon day is the first day of the month, the beginning of months. These days never, ever, ever overlaps each other on God’s Time! ........However, this is not true on the famous Gregorian calendar. The new moon day falls anywhere and everywhere on that calendar, in a given month. For example, sometimes, the new moon day falls on a “man made Saturday Sabbath”, on a “man made Sunday Sabbath”, in the midst of the month, etc. How can it both be the first day of the month and the seventh day Sabbath? How can the first day of the month start in the midst of a month? God said in Genesis 1:14 to, let the lights in heaven be for days, etc. So, which one or ones of God’s three category of days are kept by the lights in heaven? ...The new moon day? ...The six work days? ...The Sabbath day? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Example of God’s months: 1st week... new moon day, six work days and Sabbath day 2nd, 3rd, 4th weeks....six work days and Sabbath day The next month the cycle starts over. God’s months reset. Read Luke 6:1 Man uses this same concept. For example: The 1st and 3rd Sunday in August, the 1st and 3rd Sunday in September.” “The 2nd and 4th Sabbath in April, the 2nd and 4th Sabbath in May.” Note: There is never, never, ever, ever, 5 weekly Sabbaths in any one of God’s months. This is not true on the Gregorian calendar. Sometimes, there are 5 weekly “Gregorian Sabbaths.” This is not in align with true time. ~~~~~~~~~~~~~~~~~~~~~~~~~~ I believe there is a great deception coming to get people to worship Satan through a false Calendar/Sabbath controversy. God is a God of truth. God guides people by His truth. God’s Word is truth. Truth is our shield and buckler. Truth will keep us from all deceptions, the mark of beast, etc. Christ did not suffer on the cross for us to walk in a lie and continue to cling to our traditions! He did not die for us to keep obeying the “voice of man” above “the voice of God!” Read the stories about “King Saul” in 1 Samuel 15 and the “man of God” in 1 king 13. Let us learn a lesson from these testimonies....Obey God’s Voice! When we do and teach man’s commandments for doctrine, it is vain! It is useless! God does not honor it! There will be no reward! Again! there is a great possibility some type of “Man made Sabbath Law” could be enforced. These latter days crises seems to be pointing in that direction. If this is not true, then, we do not have to worry about it......But..... ....If it is truth then, we need to become more knowledgeable about this subject in order to make the right decision whom we will honor and serve. A Sabbath test will reveal those who believe Gods Word in Genesis 1:14 and those who do not believe His Word. Whether there is or whether there is not a “Sabbath Test”, we still need to know the truth about God’s Time written in the Word of God so we can be obedient in all things. ***Worship Him that made heaven, earth and sea. ***Babylon is fallen! Babylon is fallen! ***Do not worship the Beast and receive his mark, whosoever does, will be eternal lost and be burnt with fire and brimstones. ****Read Revelation 13 & 14 This truth about God’s Calendar/Time and The Sabbath written in Genesis 1:14, Leviticus 23:1-3, Psalms 104:19, etc.is spreading throughout the four corners of the earth. This message enrages many who claim to be followers of Christ because they can not refute it. It seems, the people outside the church buildings are the ones eagerly accepting it and believing it. Please let us consider what is being said here and further research this important subject before it is to late. Peace and Love Friends of God

[@thandekazirema4508]

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

[@elladuarte8469]

Thank you sooooo much for making math soooo easy! I had a phobia to numbers until now! 🥰🥰

[@eccentricorgan]

This lesson was a "light bulb turning on" moment for me. THANK YOU!

[@emmanuelagwu6730]

You are just exceptional and incomparable sir . I esteem your great numerical prowess

[@jchrg2336]

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

[@susanthursdays5008]

Ive been wanting to find a concise and comprehensive ‘lesson’ on finding ‘square roots’, .. this came up. Bang! Does the job! Ty!!

[@MathAndScience]

Welcome!

[@gadgetsmall6103]

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.

[@nicoletassin7307]

Great for beginners and as a refresher! No extraneous talking....straight to the points! Thank you!

[@joyunday1167]

You're far better than actual school. Thank you for sharing your knowledge.

[@KENMATH]

Follow me on my channel (Math puzzle &is 1+1=3) a lot more coming ahead kzbin.info/www/bejne/ol7ZoHp5gphohq8 kzbin.info/www/bejne/jpu6eq16ZpWCrpY

[@ruthjulian9908]

Hi

[@tammyschilling5362]

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.

[@MathAndScience]

Thank you Tammy!

[@cherylglaze8706]

Very helpful.....great explanation!!!! Thanks

[@eliagolia1]

Sir! you have the great gift of teaching! thanks!

[@ronyon2791]

it's so easy to understand. a very good teacher indeed !

[@TexasDesert3523]

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.

[@eciruamttenrub5523]

What a great teacher!

[@roguishowl3915]

Thank you this is what I was looking for. Excellent video lesson.

[@stevesteve7175]

Great teacher. He makes it so simple.

[@chelseawillis9259]

Seriously thank you so much!! My videos for my algebra class did not explain this well and FINALLY found a KZbin video that helped!! Please keep posting!! Will definitely be back to look for more videos!! :) :)

[@mariedelsoin2195]

thank you for teaching and you are a great teacher

[@ApexMark2002]

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."

[@nextblip]

I have also leaned about orphaned number as well. Thank you again :-) m a fan of yours.

[@jayvega2206]

Out of all the videos I watched this is the one that helped me.. Thank you so much!😉

[@strikergamerz9780]

I love your videos. I didn’t understood what’s a square root, but after this video I understood what’s it… thank you

[@juratejurate1940]

Best of the best ‼️Thanks for your amazing videos and amazing teaching ‼️

[@MathAndScience]

Thank you!

[@xelaju8]

My second lesson of the day. Very interesting. Thank you.

[@KENMATH]

Follow me on my channel (Math puzzle &is 1+1=3) a lot more coming ahead kzbin.info/www/bejne/ol7ZoHp5gphohq8 kzbin.info/www/bejne/jpu6eq16ZpWCrpY

[@user-kt7vg7wv8k]

best math video ever i dont even need a teacher anymore thank u so much

[@cathydodds-bully6288]

I learnt more in this video than 5 of my math teacher classes

[@emiliojr.cabandon6257]

IT'S BECAUSE YOU'RE MUCH WISER NOW THAN YOU WERE YOUNGER THEN.

[@drobinson2694]

thank you, this was helpful as I am homeschool my son, I have a better understanding of radicals and radicands

[@itzal6205]

thank you for this explanation sooo HELPFUL! :)

[@KENMATH]

Follow me on my channel (Math puzzle &is 1+1=3) a lot more coming ahead kzbin.info/www/bejne/ol7ZoHp5gphohq8 kzbin.info/www/bejne/jpu6eq16ZpWCrpY

[@dayanaluna1411]

Thank you very much i can understand now totally worth watching this whole 42 min lesson👍

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Wow! I adore your teaching so much

[@thoughtfully]

I never did get this until now. Thank you.

[@llkingproductionsl2154]

It feels like an actual class

[@etnub]

True

[@intodacold]

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!

[@charlesebere297]

Thanks for the tutorial

[@rubeniamalone3810]

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.

[@curioussteve]

GOOD JOB YOU DESERVE AN AWARD.

[@sarahkuhne2212]

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💡

[@thatboyjennifer8669]

thats why all 540,999 are here

[@franklozano5037]

omg thank you!! had a light bulb moment! you're brilliant!!

[@joycemeadows9837]

Thank you for breaking it down. I was stuck and now this makes perfect sense.

[@x-tremeadi1110]

You are the best teacher i have ever seen

[@alexgrant2931]

This teacher is excellent!

[@erinekim]

You’re a great teacher!!

[@thechaffers6393]

Principle Square Root. Thanks for this!

[@anjumahamed5678]

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.

[@Ynkneodb133]

Thank you for this video! I really understood what you said

[@joanmelnick1704]

This definitely needs to have been taught in grade school, college, etc. This is making math fun.

[@shawnd.8498]

Genius! I understand it perfectly.

[@tariqmahmood6719]

God blessed you. Excellent teacher

[@janiking265]

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

[@MathAndScience]

Thank you!

[@Whispering_Petals30]

I just started grade 6 and knew nothing about square roots at all, this guy made this chap look so easy, thankyou so much 💞💞

[@criseastman6503]

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!

[@gregorykotoch5045]

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.

[@burntt999]

this was just great. thank you.. helped me out a lot

[@charlenegp8266]

EXCELLENT! TALKING IS GOOD! THANK YOU FOR TAKING YOUR TIME.

[@rakeshraman4380]

Good Day, Sir. A very good lesson. Explained well, Sir. Thanks for your video.

[@sidneydesouza9575]

Love it the light at the end.thank you.

[@curiosityfuels661]

OMG THANK YOU🙌🙌 I went through 6 videos and 2 days and saw your video AND I GOT IT😁

[@isaacaliakor4735]

I cannot thank you more than enough sir

[@henryfayol6667]

Clearly understood thank you so much

[@frankelizalde9306]

For working factor tree, good practice is to find the largest number, OTHER than one, to start the tree work.

[@felixyongco1168]

The best teacher. All very ,very very clear. Thank you sir.

[@kevinmosgo5492]

You are an absolutely incredible teacher!

[@xxnuttybuddyxx]

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.

[@lizfernan9701]

Wow! Thank you! Great teacher

[@1sneakycat]

Great video. Learned more on this video than I ever learned in school.

[@user-he7kn9zi4q]

thanks😍😍

[@mohammedhafiz3137]

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

[@alexandriaclark-rowe8777]

Thank you! This was very helpful and refreshing !

[@asenciondivinagracia8248]

Nice..sir...i love the way u explain

[@Abbababy.]

Even after 2yrs I still come back here to learn kudos man your the best🎉

[@Little.Flowerbloom]

I wish I would have had a teacher like this man growing up!!!

[@Mathefusions18]

The explanation is precise. Great maths.

[@winfieldbrathwaite73TonyTruth]

I LOVE YOUR TEACHING it is optimal and commendable

[@Nrecipesanddailyvlog]

just awesome explanation.Thankyou sir.God bless you.

[@Mari-kj9rt]

This was so helpful. I shared it with my classmates!