Square Roots, Cube Roots, and Other Roots

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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[dontstealmydiamondsv]

That dopamine hit when getting the right answer never gets old

[karms]

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

[hellfrozen]

This one's hard to wrap your head around

[cdpalmo]

im halfway through this playlist, you’re a lifesaver prof

[vaishanthjv]

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.

[Kain]

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...

[jamacianvncecuh]

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

[takebacktheholyland]

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

[timsn]

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.

[deesnuty]

I regret not listening to my grade 1-10 teachers

[tramarthomas]

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

[abednegobitrus]

Thanks much Sir now I know that everything is possible you are truly the maths Messiah

[fnkymnk_]

Hello professor, Can you make a video on the proof of trigononetric ratios of combined angle

[RichardRoy]

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.

[dbleR]

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.

[fizzincore]

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.

[shreyam.b]

Honestly it's helping me a lot, it's been a weeks I'm daily watching it nd I am soo eager to finish all the videos till last.. because my brain is going to work nd I will not be anymore average student 🥹, nd the most interesting is this all the videos are just amazing nd short which creates more interest nd thinks as it's easy, for any students who wants to start with basic.. thank you soo much, you are like a god that you helped a lot.. because maths is a subject where you need a deep understanding nd basic clear to understand the advance level equations or whatever it is..

[Kor]

You legit taught me more than my teacher taught me all year

[snowgibson]

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

[bullpup]

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....