Why is it called a SQUARE root?

I explain why it is called a square root, and also how a square root works.

#mathematics #DoS

Clarifications:
To keep this video simple I decided to not talk about complex numbers. But perhaps I should have mentioned complex numbers when talking about the square root of negative numbers.

When I said "you can never have a square root of a negative number", I guess I could have said "you can never have a square root of a negative number, unless you use complex numbers."

Cool, well I'm still learning! And thanks for keeping me in check. :D

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[domainofscience]

Hey thanks for all the wonderful comments. For those of you who pointed out that I didn't talk about complex numbers, I think you make a fair point that I could have at least mentioned them. I wanted to keep the video simple, and so decided to just ignore complex numbers, but in hindsight I think mentioning would have been good so that people who have not heard of them before at least know they exist.

So thanks for pointing this out. I like finding out what you think works or not. :)

[michelferreira]

Square root comes from the latin origim "Radix Quadratum", which means "The side of a square".

In the beginning, they used the term "Radix quadratum 16 equalis 4" or "The side of square 16 equals 4."

Later they made abbreviations: "r quadratum 16 = 4" and then they jumped to "r16 = 4" and finally "√16= 4."

This "√" shaped symbol is in fact a "r" alphabet letter. A shortcut notation that is.

"Radix" in latin based language was wrongly translated to "Raiz" (because the phonetics of the words are very alike) which means "root" in English language. The correct translation term should be "Side" ("Lado" in latin based languages), not "raiz".

So, square root means "the side of a square side 16 is equal 4".

I hope that helps.

[sunirainbow]

Wow. I don't know why teachers just didn't show us what you just did when explaining square roots. It makes so much sense.

[syazanizulkhairi]

hey man, nice video.. this is exactly what students need this days.. I love videos like this that focus more on understanding than just following and memorizing .. you're teaching real math man keep it up

[andresbarriga]

Keep up the good work. This is the kind of channels we need.

[illbet]

I always wondered this but none of my teachers would ever give me a good and straight answer! Thank you for this video!

[tanoherc]

Nice video. I may only say that at the level of real numbers the square root function is defined to always take the positive choice: e.g. the square root of 25 is 5, not -5. A completely different thing is to find the roots (or zeros) of the polynomial x^2 - 25: in that case you have 5 and -5. Perhaps the similarity of the notions (and the words used to denote them) is a little confusing a priori, but they are indeed different things. Best.

[BWG]

The part about a square root being either negative or positive is false. The square root of a number is always positive, which is why the solution to x^2 = 4 is x = +/- sqrt(4) = +/- 2 - the square root of a number is defined as the positive solution to this type of equation. So if you take a number, square it and then take the square root of it you get the absolute value of that number.

[darchcruise]

I wish this YouTube channel existed when I was in school. I love it!

[atishmistry]

Big love from a maths teacher in the UK. I'll be showing this to my class!

[sebastianchem]

Dominic your videos are amazing. Please don't stop making them. I'm sure one day your channel will have millions of subscribers because your videos are just so good.

[markptak]

Nice job however I suggest some nod or mention to the fact that one can't take the square root of a negative number only when you confine yourself to the real number system.

[venkatkotti]

You are a genius. I love those graphics. Excellent!!!!

[JW-bcuq]

Rock On! I NOW HAVE MY LIFE BACK; I was mulling over this one in my grey matter for a few weeks and none of the reference books made it understandable for me. I finally I got it in three minute. Thanks.

[eddyfirdeus]

You are amazing, I have struggled so long and never understood those things, you explain things so beautiful and all that with visualizations. Thank you so so much and please keep going making such wonderful explanations.

[Thedigitalalex]

I am so grateful to you . I had never understood this my whole life.

[panoskaoukis]

Please correct me if I'm wrong! In the video you said that a perfect square is a number that it's square root equals a whole number ! My question is : Is 0, 01 a perfect square ? Because its square root equals 0, 1 (not a whole number but neither an irrational number)

[Bicho]

I spected a explain for the "root" word

[hammadrasool]

Genius bro! That's the maths I wanted to learn at school.

[dragonzed]

I knew where the "square" part comes from, and came expecting an explanation of the "root" part, but even you mention it at the end I still have to ask ¿what is the meaning of the word "radix" in roman? :P This needs an answer!