Square Roots, Cube Roots, and Other Roots
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- Опубліковано 20 лип 2024
- What are these funny little symbols? They're roots! Taking the square root of something give you the number that, when squared, gives the original number. Cube roots are the same, but they are the opposite of cubing. I'm not explaining it very well right now, but that's what this clip is for, so watch it!
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That dopamine hit when getting the right answer never gets old
It is basicly what i live for!
motivates me so much fr
Factz lmao
Lol
Same here!
This one's hard to wrap your head around
For the answers at the end:
√16 is 4 x 4 which is how you get 4 as the answer
√50 is 5 x 5 x 2 expressed as 5√2. If you can't get the square root of a number by multiplying a smaller number by itself, there's 1 extra number you need to multiply it by to get it.
√300 = 10 x 10 x 3 which is written as 10√3
√243 = 9 x 9 x 3 = 9√3
The number you multiply by itself is written once before the square root and the total after multiplying is multiplied by the number in the square root to get the final answer.
@@karma1507 Thanks man.
@@uzairmalik007 You're welcome.
@@karma1507 that's actually super helpful for me thanks bro
@@karma1507 why not plus or minus 5√2 coz -√5×-√5×√2=√50
I'm about to begin calculus but I'm going through this amazing 'All Of It' playlist to fully understand everything from arithmetic, instead of just relying on memorization and to eliminate any bad habits I've developed. You make math fun even with these short videos and explain everything so well. Can't thank you enough @ProfessorDaveExplains
I'm also doing the same way because in engineering we use this kind of equation specially in integration
@@aarenthegamer1835what do engineers do? Can you build a gun?
@@edmundoandrade5113 engineering, the word itself means to create, build, design, invent something that is to engineer something. You can build a gun with just a rubber band, everyone has a hidden engineer in them. If you can think it you can make it, if you make it you have an engineer in you.
It's kind of funny... back when I was in school, while good at math, i didn't really pursue it past just getting decent grades and moving on...
Now here I am, 25 years later, recapping all of this stuff for both entertainment and due to the frustration that most of it is locked away in some brain dungeon since I've barely used more than arithmetic and basic algebra ever since finishing high-school. I pursued social sciences, but heck, I have engineer friends who can relate.
And now I'm brushing up on this because in some years time, when my daughter starts school, she might want to ask me about math... and I'll be damned if I'll ever be one of those parents that dismisses my child's questions because I don't know and am too stubborn to find out and help.
Regardless, math is a lot more fun when it's not compulsory...
im halfway through this playlist, you’re a lifesaver prof
The radical sign(√) refers to the principal square root of a number. So √9 = 3.
Square root of 9 is both 3 and -3, when using the radical sign it is the non-negative real root.
you can use x^(1/2) or ±√3 to refer to both the roots.
I regret not listening to my grade 1-10 teachers
Same here ,now am suffering 😞
Damn, it would have been great to have you around way back when. I love looking at different ways of presenting an idea. You never know when you're going to hit upon an approach that glues what was once a seemingly disjointed set of ideas together clearly. There's a lot of material I missed in school in this video alone. Thanks.
Thanks a million professor Dave I wouldn't be good at math if it was not for you thanks a million professor Dave.l learn a lot of lessons from you and have half a book of notes
I agree, Professor Dave is a genius in his straight-to-the point presentation. He is a gift to maths students.
Funnily enough, I completely forgot 100 was a perfect square and took the harder route to √300 by answering it as 5√12 because 300 = (12x25) √25 = 5
Hello professor, Can you make a video on the proof of trigononetric ratios of combined angle
yep, trig will come in due time!
Thanks
Quick tip I learned from a channel called Let's do math on fast long division that allows for easy mental division. Take 243 and I really a factor from it. It's an odd number, we can tell from the unites place having 3, so we divide by 3 which is a prime number. 3 divide by 2, it doesn't go into it so we carry the 2 move and treat the next number as 24. 3 divided by 24 is 8, then 3 divided by 3 is 1, so 81. It'd like like 0, then 08 then 081 on paper. If instead of 243 we had 343 and we divided by 3, then on the first step we'd get 1, and treat the 4 as if it's a regular 4. 3 goes into 4 once and we carry the remainder and treat the next number as 13. 3 goes into it 4 times and we have 114 remainder 1
Thanks much Sir now I know that everything is possible you are truly the maths Messiah
I don't know how you're on my subscription feed. Not complaining, just found it to be odd. I feel a little smarter today! Thanks from SFV.
Square roots are a function from the non-negative reals to the non-negative reals. The square root of 9 is 3. The solutions to x^2=9 are 3 and -3.
Yeah totally
Almost. The radical sign in particular is that. But the term "square root" can mean the positive square root or the negative square root, or both.
@@Mswordx23 That is why I generally use the '1/2-power' instead, which includes both.
I pointed that out, and my comment got deleted.
Such a lifesaver! Cheers bud
not sure of your experience with this but i was curious about the math involved in game development. i am not sure if there are only specific parts of areas like alegbra, trig and cal that you need to know for programming games or if understanding all formulas and concepts are needed. just pretty slow at grasping math though your videos do help out alot, easy explanations and just long enough for those with low attention spans. any thoughts and advice?
ooh sorry i don't really know anything about programming!
You'll need to know: 'Algebra, Geometry, Trigonometry, Calculus, Linear Algebra, and a little bit of Newtonian physics'. Unless you want to be constrained by the standard-setting of your game engine, it will require you to understand how objects move through space. For Mobile and Web Programming you could get away with basics algebra but being well-rounded in Math is always useful no matter what type of computer programmer you want to be!
@@ProfessorDaveExplains im really surprised that you don't know programming since you know so many scientific topics. Anyway learning programming will be a piece of cake for you.
Please do work on permutations qnd commutation and binomial theorem
i love the intro 😂
I too🤚😅
hello, not sure if you have been asked this before. thanks to simple videos like these math can actually be fun to learn. though I am bit stuck, while with practice I am understanding how things are solved. but I am always wonder what these different equations and formulas can be applied to rather then just solving random problems. have any tips or advice?
pretty much everything! the universe is math, as is everything in it.
so is it really about memorizing and practice then?
it's just about making all the math really intuitive so that you can understand how it describes the physical world when you study science, and how to use math to make predictions and build things and what not.
ah thanks
@@ProfessorDaveExplains Will square root of 16 be +-4 ,or just simply 4?
As in checking comprehenision you have assigned all square roots positive value rather than positive/negative value
I recognize the steps and how to do them, but for some reason have such a hard time conceptualizing math. I’ve gone up to calc 2 just trusting that the rules I’ve learned work and essentially memorizing all the Interacting parts, but when I try to do something like visualize what 4 to the 1/3 power really looks like it scrambles my brain and leaves me feeling like I really don’t know mathematics.
there are many methods to find square roots.Like prime factorization or long division
what is the easiest and best of all?
Electronic calculator
@@NickHope Ha!
You're awesome, dude.
Awesome sir
question if with square root of 50 lets say. shouldnt the square root be under the symbol and the cube be outside. like 5\2 then 25 times 2 on the outside? or does it really not matter which way it is writen?
sorry i don't understand the question!
all good never mind i think i figured it out.
Hello professor can you please explain deeply about the anomeric Carbon found in carbohydrates and about the mutarotation!!
this is a math tutorial, silly! and i have a tutorial on that in my biochemistry series.
@@ProfessorDaveExplains Sorry, something not related to maths again, but can you please debate Kaleb FE on flat earth because that guys needs knocking down a peg or five. Be sure to mention his electric gravity theory if you do, because that's hilarious (very easy to negate an electric force and thus gravity). And one last thing, could dark matter be the actual fabric of space that is bent by masses? I have loads of other questions. Such as do atoms contain hidden information (variable and programming as such)? Yes, they do - otherwise how would a spider know how to spin a web? How can male/female attraction work without that atomic level programming (for want of a better word). I have a million more questions but I better shut up now ...
Can someone show their work for the Checking Comprehension questions! im not to sure on what formula to use or even how to start to figure out what the square root of 50 is! HELP
Professor sir please do stuff on permutations and combinations sir
yep i've got one on that coming!
Thank you for making these easy to understand videos I got a c in algebra 1 and this is going to help with algebra 2.
can someone explain to me
(roots as afractional exponents )
Hey prof., how were you able to x^10/12 at around 7:49? I understand about x^3/12 but I'm stuck with the numerator one..
Multiplying by 2 and 3
as explained in the video he wanted to get the lowest common denominator (12) to compare the x^(5/6) with the divisor x^(1/4)
you can get that by multiplying the x^(5/6) with 2 as x^(10/12) is the same.
he then multiplied x^(1/4) with 3 to get the same exponent 12 which is x^(3/12) and that's how you get the numbers shown on the video
No technique for square root long division? And other root long division?
Taking a root is not the same thing as division so I'm not sure what you're asking.
Why sometimes we subtract X with a number and sometimes we subtract only X from that number in algebra?
I have an equation like the first in the video but 18 is under the root ... What is the solution?
If you mean x^2=18 you would do it like this:
x=sqrt(18)
x=sqrt(9*2)
x=scrt(9)*scrt(2)
x=3*scrt(2)
simply an excellent explanation
God, I know that this is the simplest explanation I can get anywhere but damn, my brain hurts even though I am very motivated to learn. Understanding the roots proved to be difficult for me even though I watched this for the 4th or 5th time(?) Maybe I am too stupid lol.
You aren't stupid. Believe in yourself!
there are other videos that "go around the houses" with longer explanations. I have to write every single step down, look at other ways of presentation then come back. It will make sense with plenty of practice examples (so I am told!) Good luck.
I know its been a while but for anyone maybe struggeling i looked at the info of 3√x^2 = x^2/3...
So the reason for this is if you look at x=4 we can put this in the equasion
2√8^2 = 8^2/3. The reason why this is the same is we can start by the first step amd just look at 3√8^2. 8^2 = 64. So that leaves 3√64. The cube root of 64 is 4. (4×4×4= 64). ×=4
If we go to 8^2/3 this is the complicated part. You can first cube root the 8 which makes 2 (2×2×2).
This leaves (2^3)^2/3. By the rules you can make this 2^3 ×^ 2/3. If we now only look at 3 × 2/3 it will make sense 2/3 + 2/3 + 2/3 =6 /3 = 2. And since it was raised this will make 2^2 which is 4 which makes x=4. Sorry if this was long but hope it helped anyone
man great video
This guy is a complete legend.
Oooo Shoot :O I'm gettin' it, Thx Prof. Dave!!
Thank u
Is there a way to simplify √5 by prime factorization?
5 is already prime, so there is no way to further factorize (caveat for the pedantic youtube commenters: in the set of real numbers)
5 is already prime
5 is already a prime number
Is it ok if the answer on √243 is 3√27?
Almost but not quite. How would you simplify √27?
@@Jeff_Segal √27=√9 * √3= 3√3
Ok. I understand what you're saying, and I did the questions and got them right. But. Logically it doesn't completely make sense...
Wouldn't the answers be squared? Doesn't 9^2√3 make more sense than just 9√3?
and also... how come it wouldn't be expressed as 9^2(3)? Wouldn't that make more sense than 9√3?
I'm genuinely curious. It took me a while to wrap my head around it to begin with. I'm glad I can calculate it now... but I wish it made logical sense in my head
When you use the radical sign you are asking for the principal square root (the non-negative square root of the number). So while the square root of 4 is +2 and -2, the radical of 4 has only one answer 2 .
Yes you are right mabrthrax
Thnkuuu
A comment of mine seems to have been deleted, was I wrong in pointing what I did?
ty
I'm a bit confused as to how he instantly went to 3/6 and 2/6 can someone explain?
Minute: 7:35
i think multiply both denominators first (2 and 3) then proceed to cross multiply for the numerators
This is an example where mathematicians should get their act together and agree on a consensus. In Germany, only the positive values are considered roots. Sometimes, a distinction between root and root function or radical is made. You don't make the distinction. It's confusing....
That's weird. If only the positive value is considered the root, how do you deal with the fact that the negative answer works too?
8:25 the answers should have ± ???
I love your videos!!
The sqrt function has only the primary root.
✓9=3 not -3
I never thought that a guy that looks like a discord admin (no offense) would make me 10x smarter than i was literally 3 days ago, thanks man.
Shouldn't the answers to the question in the end be +/-?
Why in the answers in the comprehension are not given in +-
He didnt explains it in this video but although we have 2 square for every nonnegative real numbers we only take the positive one and it is called the principal square root we dont write the negative solution unless we are solving equation that we need to take the square on both of the equation hope did explains it well
To expand on Chikla Chiklas answer: There is a reason we have a "principal square root" and only consider the positive value when taking the square root.
Consider the equation x^2=16. "Solving" this equation means finding all the values of x that will make the equality true. Both x = 4 and x = -4 will work, and you can convince yourself of this by replacing x with this values in the original equation.
Now consider the operation sqrt(x) like we have in the comprehension exersices. For every value of x you choose, you get a number back. This is what we call a function, and we decide that it is important that for every x we pick, we get only one number back. Why do we decide this? Because otherwise the function is not very usefull to us. So while both +4 and -4 is a perfectly good answer to sqrt(16), we can only pick one, and so we pick 4 because historically we are biased towards positive numbers :)
So while the two cases might at first seem the same (you solve the equation by taking the square root of both sides for instance), they are in fact seperate although related consepts.
PS. this might seem very pedantic and confusing when only reading about it, but makes much more intuitive sense if you graph (draw) the equation and function in a graphing calculator like GeoGebra or Desmos.
why do we use square roots and not just rasing to the power of 1 over 2?
Same operation, just different notation.
Your mathematics are special because there wear not get any thingggg
Thank you so much professor dave!
For √243 could 3√27 be an answer?
that's a good partial solution but you can still simplify √27 into 3√3 so you have 3(3√3) thus you get the result show on the screen
@@redsnabba4947 how did you do it can you explain in detail ??
@@redsnabba4947 why did you take 27
@@ridmicmeena4123 The original poster commented 3√27 as their answer for √243. This answer is incomplete.
Let's simplify √243. I'll walk you through the steps and after that we'll evaluate where the original poster likely went wrong, alright?
So, what do we know about √243? Let's list it off:
- We know it is the number, that, when multiplied by itself, makes 243.
- 243 isn't a perfect square. We can tell, because numbers that end in 2, 3, 7 or 8 are never perfect squares.
- √243 can probably be simplified, because we don't like having big numbers under the √ symbol if we can help it. We want to make that number as small as possible and 243 is pretty big.
Now... what can we divide 243 by to make it smaller? If we divide it by 1, we still have 243. We can't divide it by 2 because it's uneven. What about 3? 243/3 gives us 81. In other words, √243 is the same as √(3*81).
Another way this can be written is √3 * √81. This makes sense because when you think about it, writing (3*81) means the same as writing 1*(3*81). When you write something between parentheses in math, there is an implied "1 times" in front of it. We just don't write it down because it's superfluous. But when you remember that it's there, you can easily solve for √(3*81), because it becomes √1(3*81). √1*3 = √3 and √1*81 = √81. So, √(3*81) = √3 * √81.
Can we simplify this? Yes, we can. 81 is on our times table. It is the product of 9 and 9. This makes it a perfect square.
√3*√81 = √3*9. We cannot simplify √3 because it is a prime number, and we like to put our whole numbers in front of our radicals when we multiply them, so our final answer is 9√3. It is not 3*3√3, because we can solve for 3*3.
----------------------
So how did OP get 3√27? Well, that's because the way we just did it isn't the only way to get the answer.
What else can 243 be divided by? Not 4, 5, 6, 7 or 8, but there's 9. 243/9 = 27.
"A-ha!" the original poster probably thought, "that makes √(9 * 27), or √9 * √27, and 9 is a perfect square! √9 * √27 = 3*√27, or 3√27. I am done now."
But they weren't done, because 27 is not the smallest number you can get under the √ symbol and that's what we want.
What can we divide 27 by? 3 and 9, right? So, 3√27 = 3√(3*9).
Remembering that implied "1 times" before parentheses, we solve: 3√(3*9) = 3*√1(3*9). That's 3*√3*√9. We know that 9 is a perfect square, so 3*√3*√9 = 3*√3*3.
PEMDAS says we can multiply these values in any order we want and get the same answer, meaning we can solve for 3*3 and get 9*√3. We take away the multiplication symbol because it is unnecessary and our final answer is 9√3.
Different approach, same answer.
I'm going to refer you to my answer to Ridmic Meena above. I hope this helps!
How did x^10/12 / x^3/12 became x^7/12 anyone explain
Because you want to simplify it and get rid of the fraction so you subtract x^3/12 from x^10/12 which will be x^7/12
things went from cheese to biriani real fast in this video
😢sameee
√50 =7√1 sir is it wrong or correct?
Yes brother, right answer is 5√2
@TERA EDGE - تيرا ادج
3-x=17
-x+3=17
-x+3-3=17-3
-x=14
x=-14 Answer, very tricky question brother 🔥
√50=√(2*5*5)= √ (2*5^2) = 5√2
@@Chulbooli.131 3-x=17
3=17+X
3-17=X
X=-14
@@luish1498 yes brother you are correct
Done.
literally never understood sqrts until 9th grade
√27 is 5.1615242270
7:44 how??????😭😭
5/6-1/4
lowest common multiple of the denominators 6 and 4 is 12
6 (2) = 12
4 (3) = 12
and you just multiply their numerators the same amount
5 (2) = 10
therefore
10/12
1(3) = 3
therefore
3/12
since they now have common denominators they can be subtracted
10/12 - 3/12 = 7/12
You're sure it ain't the contrary ? 🤔🤔🤔
You are teaching wrong. Root(4)=2... not plus minus does not appear here. When x^2=4 then x=+_2
Root(4) is also -2
Sir you need to improve the level.It took me 0.6 seconds to solve all these.
ok buddy, everyone is at a different level with math! this tutorial is for people who are not familiar with this concept. i promise that eventually i'll be doing math that you find challenging.
Professor Dave Explains Thanks sir.Also try to include a bit of SAT related problems.
there are already a lot of challenging questions out there. answer those, because people like me is still developing my math skills. no hate, just saying.
"I have a lamborghini and find toyota camry's too easy to race!"